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1.0.0 | problem:theoremdb-p5524 | problem | theoremdb-p5524 | Clique number of the Paley graph of order 2017 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2017)$ be the graph on $\mathbb{F}_{2017}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2017$. Determine the clique number $\omega(P(2017))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5524",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5524",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5524 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5524",
"url": "https://theoremdb.org/statements/P5524",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5524",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:30:44+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5524,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.069Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"139f407b-8a86-4b4c-b5f7-c41ab26a996f","format_issues":null,"number":3778} |
1.0.0 | problem:theoremdb-p5526 | problem | theoremdb-p5526 | Clique number of the Paley graph of order 2029 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2029)$ be the graph on $\mathbb{F}_{2029}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2029$. Determine the clique number $\omega(P(2029))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5526",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5526",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5526 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5526",
"url": "https://theoremdb.org/statements/P5526",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5526",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:30:48+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5526,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.073Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c6959494-59fe-480d-b986-63a1ac4e4cd7","format_issues":null,"number":3779} |
1.0.0 | problem:theoremdb-p5528 | problem | theoremdb-p5528 | Clique number of the Paley graph of order 2053 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2053)$ be the graph on $\mathbb{F}_{2053}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2053$. Determine the clique number $\omega(P(2053))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5528",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5528",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5528 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5528",
"url": "https://theoremdb.org/statements/P5528",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5528",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:30:53+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5528,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.077Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3dbd48ee-1618-4f53-ad58-1723d10defa3","format_issues":null,"number":3780} |
1.0.0 | problem:theoremdb-p5530 | problem | theoremdb-p5530 | Clique number of the Paley graph of order 2069 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2069)$ be the graph on $\mathbb{F}_{2069}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2069$. Determine the clique number $\omega(P(2069))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5530",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5530",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5530 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5530",
"url": "https://theoremdb.org/statements/P5530",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5530",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:30:58+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5530,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.082Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"11afb1c1-1873-42b3-9857-30fd5b445821","format_issues":null,"number":3781} |
1.0.0 | problem:theoremdb-p5532 | problem | theoremdb-p5532 | Clique number of the Paley graph of order 2081 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2081)$ be the graph on $\mathbb{F}_{2081}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2081$. Determine the clique number $\omega(P(2081))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5532",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5532",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5532 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5532",
"url": "https://theoremdb.org/statements/P5532",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5532",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:31:05+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5532,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.086Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8c856f4e-b5d9-41e7-922a-d410e14f7fa7","format_issues":null,"number":3782} |
1.0.0 | problem:theoremdb-p5534 | problem | theoremdb-p5534 | Clique number of the Paley graph of order 2089 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2089)$ be the graph on $\mathbb{F}_{2089}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2089$. Determine the clique number $\omega(P(2089))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5534",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5534",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5534 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5534",
"url": "https://theoremdb.org/statements/P5534",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5534",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:31:12+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5534,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.090Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c2d0750c-1e35-4608-8357-4fa616c9ab0c","format_issues":null,"number":3783} |
1.0.0 | problem:theoremdb-p5536 | problem | theoremdb-p5536 | Clique number of the Paley graph of order 2113 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2113)$ be the graph on $\mathbb{F}_{2113}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2113$. Determine the clique number $\omega(P(2113))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5536",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5536",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5536 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5536",
"url": "https://theoremdb.org/statements/P5536",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5536",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:31:18+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5536,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.095Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f7c5db34-4890-4fd2-9f39-258207e2425b","format_issues":null,"number":3784} |
1.0.0 | problem:theoremdb-p5538 | problem | theoremdb-p5538 | Clique number of the Paley graph of order 2129 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2129)$ be the graph on $\mathbb{F}_{2129}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2129$. Determine the clique number $\omega(P(2129))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5538",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5538",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5538 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5538",
"url": "https://theoremdb.org/statements/P5538",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5538",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:31:26+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5538,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.099Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"fcfbcc21-14c0-4432-ba86-8d23c5cae203","format_issues":null,"number":3785} |
1.0.0 | problem:theoremdb-p5540 | problem | theoremdb-p5540 | Clique number of the Paley graph of order 2137 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2137)$ be the graph on $\mathbb{F}_{2137}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2137$. Determine the clique number $\omega(P(2137))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5540",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5540",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5540 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5540",
"url": "https://theoremdb.org/statements/P5540",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5540",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:31:36+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5540,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.103Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9c4fa62e-18b7-445c-b9f5-aad0ffb358a3","format_issues":null,"number":3786} |
1.0.0 | problem:theoremdb-p5544 | problem | theoremdb-p5544 | Clique number of the Paley graph of order 2141 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2141)$ be the graph on $\mathbb{F}_{2141}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2141$. Determine the clique number $\omega(P(2141))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5544",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5544",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5544 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5544",
"url": "https://theoremdb.org/statements/P5544",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5544",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:34:22+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5544,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.107Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3ebdeffb-a306-4267-87ab-b3df9932d395","format_issues":null,"number":3787} |
1.0.0 | problem:theoremdb-p5546 | problem | theoremdb-p5546 | Clique number of the Paley graph of order 2153 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2153)$ be the graph on $\mathbb{F}_{2153}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2153$. Determine the clique number $\omega(P(2153))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5546",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5546",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5546 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5546",
"url": "https://theoremdb.org/statements/P5546",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5546",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:34:53+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5546,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.112Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"74d22f13-2b59-4b55-a630-eefab034baa3","format_issues":null,"number":3788} |
1.0.0 | problem:theoremdb-p5548 | problem | theoremdb-p5548 | Clique number of the Paley graph of order 2161 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2161)$ be the graph on $\mathbb{F}_{2161}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2161$. Determine the clique number $\omega(P(2161))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5548",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5548",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5548 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5548",
"url": "https://theoremdb.org/statements/P5548",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5548",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:35:02+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5548,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.117Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3ba4a326-1d5f-4ca4-be1d-4d688f2f6a23","format_issues":null,"number":3789} |
1.0.0 | problem:theoremdb-p5550 | problem | theoremdb-p5550 | Clique number of the Paley graph of order 2213 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2213)$ be the graph on $\mathbb{F}_{2213}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2213$. Determine the clique number $\omega(P(2213))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5550",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5550",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5550 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5550",
"url": "https://theoremdb.org/statements/P5550",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5550",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:35:06+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5550,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.121Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"08bb18a2-2860-44bb-9a02-a009082abfe6","format_issues":null,"number":3790} |
1.0.0 | problem:theoremdb-p5552 | problem | theoremdb-p5552 | Clique number of the Paley graph of order 2221 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2221)$ be the graph on $\mathbb{F}_{2221}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2221$. Determine the clique number $\omega(P(2221))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5552",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5552",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5552 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5552",
"url": "https://theoremdb.org/statements/P5552",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5552",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:35:17+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5552,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.125Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d408a085-3009-4fb1-9a44-860e650f90e4","format_issues":null,"number":3791} |
1.0.0 | problem:theoremdb-p5554 | problem | theoremdb-p5554 | Clique number of the Paley graph of order 2237 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2237)$ be the graph on $\mathbb{F}_{2237}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2237$. Determine the clique number $\omega(P(2237))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5554",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5554",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5554 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5554",
"url": "https://theoremdb.org/statements/P5554",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5554",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:35:29+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5554,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.129Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4e5ac86f-5cf8-4636-b0ce-1e74d9b3d405","format_issues":null,"number":3792} |
1.0.0 | problem:theoremdb-p5556 | problem | theoremdb-p5556 | Clique number of the Paley graph of order 2269 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2269)$ be the graph on $\mathbb{F}_{2269}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2269$. Determine the clique number $\omega(P(2269))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5556",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5556",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5556 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5556",
"url": "https://theoremdb.org/statements/P5556",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5556",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:35:42+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5556,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.134Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f7199221-699b-421f-8232-5a084f901c2a","format_issues":null,"number":3793} |
1.0.0 | problem:theoremdb-p5558 | problem | theoremdb-p5558 | Clique number of the Paley graph of order 2273 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2273)$ be the graph on $\mathbb{F}_{2273}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2273$. Determine the clique number $\omega(P(2273))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5558",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5558",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5558 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5558",
"url": "https://theoremdb.org/statements/P5558",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5558",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:35:52+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5558,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.138Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"a46cf336-c0e9-4eed-b43a-959d4053bdce","format_issues":null,"number":3794} |
1.0.0 | problem:theoremdb-p5560 | problem | theoremdb-p5560 | Clique number of the Paley graph of order 2281 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2281)$ be the graph on $\mathbb{F}_{2281}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2281$. Determine the clique number $\omega(P(2281))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5560",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5560",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5560 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5560",
"url": "https://theoremdb.org/statements/P5560",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5560",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:36:04+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5560,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.143Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"de9a595f-4353-4e81-9eb4-ac959e078296","format_issues":null,"number":3795} |
1.0.0 | problem:theoremdb-p5562 | problem | theoremdb-p5562 | Clique number of the Paley graph of order 2293 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2293)$ be the graph on $\mathbb{F}_{2293}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2293$. Determine the clique number $\omega(P(2293))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5562",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5562",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5562 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5562",
"url": "https://theoremdb.org/statements/P5562",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5562",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:36:14+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5562,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.147Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d1200f46-fced-4703-9e80-3c4ed2f21249","format_issues":null,"number":3796} |
1.0.0 | problem:theoremdb-p5564 | problem | theoremdb-p5564 | Clique number of the Paley graph of order 2297 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2297)$ be the graph on $\mathbb{F}_{2297}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2297$. Determine the clique number $\omega(P(2297))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5564",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5564",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5564 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5564",
"url": "https://theoremdb.org/statements/P5564",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5564",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:36:23+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5564,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.151Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9e599e2d-a3e8-44da-be4a-028ca6d0c630","format_issues":null,"number":3797} |
1.0.0 | problem:theoremdb-p5566 | problem | theoremdb-p5566 | Clique number of the Paley graph of order 2309 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2309)$ be the graph on $\mathbb{F}_{2309}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2309$. Determine the clique number $\omega(P(2309))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5566",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5566",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5566 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5566",
"url": "https://theoremdb.org/statements/P5566",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5566",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:36:35+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5566,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.155Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"cea1f9cc-1512-457e-a321-7c09f117b8ea","format_issues":null,"number":3798} |
1.0.0 | problem:theoremdb-p5568 | problem | theoremdb-p5568 | Clique number of the Paley graph of order 2333 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2333)$ be the graph on $\mathbb{F}_{2333}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2333$. Determine the clique number $\omega(P(2333))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5568",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5568",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5568 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5568",
"url": "https://theoremdb.org/statements/P5568",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5568",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:36:45+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5568,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.159Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d9e58358-ccc1-40ed-920d-5e7e8e68ca85","format_issues":null,"number":3799} |
1.0.0 | problem:theoremdb-p5572 | problem | theoremdb-p5572 | Clique number of the Paley graph of order 2341 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2341)$ be the graph on $\mathbb{F}_{2341}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2341$. Determine the clique number $\omega(P(2341))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5572",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5572",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5572 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5572",
"url": "https://theoremdb.org/statements/P5572",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5572",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:43+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5572,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.164Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e0ab44da-d68f-4433-b66b-3253f50cb22e","format_issues":null,"number":3800} |
1.0.0 | problem:theoremdb-p5574 | problem | theoremdb-p5574 | Clique number of the Paley graph of order 2357 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2357)$ be the graph on $\mathbb{F}_{2357}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2357$. Determine the clique number $\omega(P(2357))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5574",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5574",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5574 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5574",
"url": "https://theoremdb.org/statements/P5574",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5574",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:45+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5574,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.168Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5d9f65ce-9534-495e-965c-a7489feae63e","format_issues":null,"number":3801} |
1.0.0 | problem:theoremdb-p5576 | problem | theoremdb-p5576 | Clique number of the Paley graph of order 2377 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2377)$ be the graph on $\mathbb{F}_{2377}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2377$. Determine the clique number $\omega(P(2377))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5576",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5576",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5576 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5576",
"url": "https://theoremdb.org/statements/P5576",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5576",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:45+00:00","display_standard":{"formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5576,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean":{"kernelAccepted":false,"label":"","rea... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.172Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ad8ce93d-dbc9-4362-bfd9-bc8a580430f7","format_issues":null,"number":3802} |
1.0.0 | problem:theoremdb-p5578 | problem | theoremdb-p5578 | Clique number of the Paley graph of order 2381 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2381)$ be the graph on $\mathbb{F}_{2381}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2381$. Determine the clique number $\omega(P(2381))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5578",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5578",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5578 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5578",
"url": "https://theoremdb.org/statements/P5578",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5578",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:45+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5578,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.178Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d481e7b9-9389-4a22-8e87-1088e1aa5f5b","format_issues":null,"number":3803} |
1.0.0 | problem:theoremdb-p5580 | problem | theoremdb-p5580 | Clique number of the Paley graph of order 2389 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2389)$ be the graph on $\mathbb{F}_{2389}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2389$. Determine the clique number $\omega(P(2389))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5580",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5580",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5580 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5580",
"url": "https://theoremdb.org/statements/P5580",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5580",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:46+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5580,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.182Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"79adb6f2-95be-4496-8714-65b9bdf1839d","format_issues":null,"number":3804} |
1.0.0 | problem:theoremdb-p5582 | problem | theoremdb-p5582 | Clique number of the Paley graph of order 2393 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2393)$ be the graph on $\mathbb{F}_{2393}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2393$. Determine the clique number $\omega(P(2393))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5582",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5582",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5582 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5582",
"url": "https://theoremdb.org/statements/P5582",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5582",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:46+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5582,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.189Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"8517250d-0c0b-47fa-83c6-e393bddfbda1","format_issues":null,"number":3805} |
1.0.0 | problem:theoremdb-p5584 | problem | theoremdb-p5584 | Clique number of the Paley graph of order 2417 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2417)$ be the graph on $\mathbb{F}_{2417}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2417$. Determine the clique number $\omega(P(2417))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5584",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5584",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5584 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5584",
"url": "https://theoremdb.org/statements/P5584",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5584",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:47+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5584,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.194Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b2690bd9-51e5-49bb-b3f4-cce5dde947ba","format_issues":null,"number":3806} |
1.0.0 | problem:theoremdb-p5586 | problem | theoremdb-p5586 | Clique number of the Paley graph of order 2437 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2437)$ be the graph on $\mathbb{F}_{2437}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2437$. Determine the clique number $\omega(P(2437))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5586",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5586",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5586 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5586",
"url": "https://theoremdb.org/statements/P5586",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5586",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:47+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5586,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.198Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3b04864d-a383-4c6f-beba-0e31bbf7ebc3","format_issues":null,"number":3807} |
1.0.0 | problem:theoremdb-p5588 | problem | theoremdb-p5588 | Clique number of the Paley graph of order 2441 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2441)$ be the graph on $\mathbb{F}_{2441}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2441$. Determine the clique number $\omega(P(2441))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5588",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5588",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5588 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5588",
"url": "https://theoremdb.org/statements/P5588",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5588",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:48+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5588,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.202Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"91bc07d5-9885-4191-9c59-9af767a331e3","format_issues":null,"number":3808} |
1.0.0 | problem:theoremdb-p5590 | problem | theoremdb-p5590 | Clique number of the Paley graph of order 2473 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2473)$ be the graph on $\mathbb{F}_{2473}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2473$. Determine the clique number $\omega(P(2473))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5590",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5590",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5590 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5590",
"url": "https://theoremdb.org/statements/P5590",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5590",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:40:50+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5590,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.206Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5bf104fb-babe-4263-bb72-e99bf8e9e820","format_issues":null,"number":3809} |
1.0.0 | problem:theoremdb-p5592 | problem | theoremdb-p5592 | Clique number of the Paley graph of order 2477 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2477)$ be the graph on $\mathbb{F}_{2477}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2477$. Determine the clique number $\omega(P(2477))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5592",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5592",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5592 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5592",
"url": "https://theoremdb.org/statements/P5592",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5592",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:41:06+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5592,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.211Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"59b1350e-a702-4a37-a27b-8b6f14ed4ce3","format_issues":null,"number":3810} |
1.0.0 | problem:theoremdb-p5594 | problem | theoremdb-p5594 | Clique number of the Paley graph of order 2521 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2521)$ be the graph on $\mathbb{F}_{2521}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2521$. Determine the clique number $\omega(P(2521))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5594",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5594",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5594 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5594",
"url": "https://theoremdb.org/statements/P5594",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5594",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:41:25+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5594,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.215Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e6d12be4-1db4-4fb6-8778-2d2a0c85cf59","format_issues":null,"number":3811} |
1.0.0 | problem:theoremdb-p5596 | problem | theoremdb-p5596 | Clique number of the Paley graph of order 2549 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2549)$ be the graph on $\mathbb{F}_{2549}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2549$. Determine the clique number $\omega(P(2549))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5596",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5596",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5596 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5596",
"url": "https://theoremdb.org/statements/P5596",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5596",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:41:57+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5596,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.220Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d2f50259-e229-41fa-8202-d7c9b0498698","format_issues":null,"number":3812} |
1.0.0 | problem:theoremdb-p5598 | problem | theoremdb-p5598 | Clique number of the Paley graph of order 2557 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2557)$ be the graph on $\mathbb{F}_{2557}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2557$. Determine the clique number $\omega(P(2557))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5598",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5598",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5598 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5598",
"url": "https://theoremdb.org/statements/P5598",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5598",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:42:13+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5598,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.224Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"847429ec-5b55-484d-b031-b686eb2de542","format_issues":null,"number":3813} |
1.0.0 | problem:theoremdb-p5600 | problem | theoremdb-p5600 | Clique number of the Paley graph of order 2593 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2593)$ be the graph on $\mathbb{F}_{2593}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2593$. Determine the clique number $\omega(P(2593))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5600",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5600",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5600 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5600",
"url": "https://theoremdb.org/statements/P5600",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5600",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:42:27+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5600,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.228Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3ba219fb-868a-4413-98b5-4d0067de9459","format_issues":null,"number":3814} |
1.0.0 | problem:theoremdb-p5602 | problem | theoremdb-p5602 | Clique number of the Paley graph of order 2609 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2609)$ be the graph on $\mathbb{F}_{2609}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2609$. Determine the clique number $\omega(P(2609))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5602",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5602",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5602 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5602",
"url": "https://theoremdb.org/statements/P5602",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5602",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:42:41+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5602,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.232Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"772382f5-c597-44b5-93bc-ac83d1938516","format_issues":null,"number":3815} |
1.0.0 | problem:theoremdb-p5604 | problem | theoremdb-p5604 | Clique number of the Paley graph of order 2617 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2617)$ be the graph on $\mathbb{F}_{2617}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2617$. Determine the clique number $\omega(P(2617))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5604",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5604",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5604 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5604",
"url": "https://theoremdb.org/statements/P5604",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5604",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:42:51+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5604,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.237Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1b752ae8-4e25-4d2e-aa6f-df552b6e42e9","format_issues":null,"number":3816} |
1.0.0 | problem:theoremdb-p5606 | problem | theoremdb-p5606 | Clique number of the Paley graph of order 2621 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2621)$ be the graph on $\mathbb{F}_{2621}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2621$. Determine the clique number $\omega(P(2621))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5606",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5606",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5606 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5606",
"url": "https://theoremdb.org/statements/P5606",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5606",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:42:58+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5606,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.241Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e2a4cbda-ca2c-48b5-927f-9cd63ff7f6e0","format_issues":null,"number":3817} |
1.0.0 | problem:theoremdb-p5608 | problem | theoremdb-p5608 | Clique number of the Paley graph of order 2633 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2633)$ be the graph on $\mathbb{F}_{2633}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2633$. Determine the clique number $\omega(P(2633))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5608",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5608",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5608 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5608",
"url": "https://theoremdb.org/statements/P5608",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5608",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:43:04+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5608,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.245Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"63e52b3d-6e70-466d-a65a-f5cb6e8b046d","format_issues":null,"number":3818} |
1.0.0 | problem:theoremdb-p5610 | problem | theoremdb-p5610 | Clique number of the Paley graph of order 2657 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2657)$ be the graph on $\mathbb{F}_{2657}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2657$. Determine the clique number $\omega(P(2657))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5610",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5610",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5610 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5610",
"url": "https://theoremdb.org/statements/P5610",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5610",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:43:17+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5610,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.249Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b739c7b1-e135-4b94-99cd-dc84f49f21cb","format_issues":null,"number":3819} |
1.0.0 | problem:theoremdb-p5612 | problem | theoremdb-p5612 | Clique number of the Paley graph of order 2677 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2677)$ be the graph on $\mathbb{F}_{2677}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2677$. Determine the clique number $\omega(P(2677))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5612",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5612",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5612 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5612",
"url": "https://theoremdb.org/statements/P5612",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5612",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:43:32+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5612,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.253Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b09aaa68-59bb-4168-b874-e59307979111","format_issues":null,"number":3820} |
1.0.0 | problem:theoremdb-p5614 | problem | theoremdb-p5614 | Clique number of the Paley graph of order 2689 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2689)$ be the graph on $\mathbb{F}_{2689}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2689$. Determine the clique number $\omega(P(2689))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5614",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5614",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5614 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5614",
"url": "https://theoremdb.org/statements/P5614",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5614",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:43:50+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5614,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.258Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"15be1da1-35e3-42fb-96f4-5dde81d16325","format_issues":null,"number":3821} |
1.0.0 | problem:theoremdb-p5616 | problem | theoremdb-p5616 | Clique number of the Paley graph of order 2693 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2693)$ be the graph on $\mathbb{F}_{2693}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2693$. Determine the clique number $\omega(P(2693))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5616",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5616",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5616 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5616",
"url": "https://theoremdb.org/statements/P5616",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5616",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:02+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5616,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.262Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ff3ea5ad-05bb-442b-8ada-a50d3449a232","format_issues":null,"number":3822} |
1.0.0 | problem:theoremdb-p5618 | problem | theoremdb-p5618 | Clique number of the Paley graph of order 2713 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2713)$ be the graph on $\mathbb{F}_{2713}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2713$. Determine the clique number $\omega(P(2713))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5618",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5618",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5618 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5618",
"url": "https://theoremdb.org/statements/P5618",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5618",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:09+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5618,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.266Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"602ea2a9-9a16-4181-88fc-76e54ac25f76","format_issues":null,"number":3823} |
1.0.0 | problem:theoremdb-p5620 | problem | theoremdb-p5620 | Clique number of the Paley graph of order 2729 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2729)$ be the graph on $\mathbb{F}_{2729}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2729$. Determine the clique number $\omega(P(2729))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5620",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5620",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5620 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5620",
"url": "https://theoremdb.org/statements/P5620",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5620",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:11+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5620,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.271Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b7b05a40-4ff4-4acd-86fc-4af45543486b","format_issues":null,"number":3824} |
1.0.0 | problem:theoremdb-p5622 | problem | theoremdb-p5622 | Clique number of the Paley graph of order 2741 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2741)$ be the graph on $\mathbb{F}_{2741}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2741$. Determine the clique number $\omega(P(2741))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5622",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5622",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5622 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5622",
"url": "https://theoremdb.org/statements/P5622",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5622",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:13+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5622,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.275Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7814bfbc-ef75-4432-a992-994472257c8f","format_issues":null,"number":3825} |
1.0.0 | problem:theoremdb-p5624 | problem | theoremdb-p5624 | Clique number of the Paley graph of order 2749 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2749)$ be the graph on $\mathbb{F}_{2749}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2749$. Determine the clique number $\omega(P(2749))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5624",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5624",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5624 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5624",
"url": "https://theoremdb.org/statements/P5624",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5624",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:15+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5624,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.279Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f03f60a8-987f-4251-b94f-da6e8618676c","format_issues":null,"number":3826} |
1.0.0 | problem:theoremdb-p5626 | problem | theoremdb-p5626 | Clique number of the Paley graph of order 2753 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2753)$ be the graph on $\mathbb{F}_{2753}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2753$. Determine the clique number $\omega(P(2753))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5626",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5626",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5626 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5626",
"url": "https://theoremdb.org/statements/P5626",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5626",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:19+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5626,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.284Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c84a1610-1074-48ad-9db6-aa8b4d594c09","format_issues":null,"number":3827} |
1.0.0 | problem:theoremdb-p5628 | problem | theoremdb-p5628 | Clique number of the Paley graph of order 2777 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2777)$ be the graph on $\mathbb{F}_{2777}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2777$. Determine the clique number $\omega(P(2777))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5628",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5628",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5628 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5628",
"url": "https://theoremdb.org/statements/P5628",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5628",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:28+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5628,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.289Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9e67b1b2-fdd9-4904-833e-8684b391437e","format_issues":null,"number":3828} |
1.0.0 | problem:theoremdb-p5630 | problem | theoremdb-p5630 | Clique number of the Paley graph of order 2789 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2789)$ be the graph on $\mathbb{F}_{2789}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2789$. Determine the clique number $\omega(P(2789))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5630",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5630",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5630 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5630",
"url": "https://theoremdb.org/statements/P5630",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5630",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:29+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5630,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.293Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3656b7d0-137f-4df7-8e1b-94dcfb8db3f5","format_issues":null,"number":3829} |
1.0.0 | problem:theoremdb-p5632 | problem | theoremdb-p5632 | Clique number of the Paley graph of order 2797 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2797)$ be the graph on $\mathbb{F}_{2797}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2797$. Determine the clique number $\omega(P(2797))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5632",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5632",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5632 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5632",
"url": "https://theoremdb.org/statements/P5632",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5632",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:31+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5632,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.297Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"93481ee8-d303-4511-8648-c47d61f481b4","format_issues":null,"number":3830} |
1.0.0 | problem:theoremdb-p5634 | problem | theoremdb-p5634 | Clique number of the Paley graph of order 2801 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2801)$ be the graph on $\mathbb{F}_{2801}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2801$. Determine the clique number $\omega(P(2801))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5634",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5634",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5634 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5634",
"url": "https://theoremdb.org/statements/P5634",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5634",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:36+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5634,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.302Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3c94a03b-d6f9-43c5-b862-06f957ed04cf","format_issues":null,"number":3831} |
1.0.0 | problem:theoremdb-p5636 | problem | theoremdb-p5636 | Clique number of the Paley graph of order 2833 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2833)$ be the graph on $\mathbb{F}_{2833}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2833$. Determine the clique number $\omega(P(2833))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5636",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5636",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5636 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5636",
"url": "https://theoremdb.org/statements/P5636",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5636",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:36+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5636,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.309Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2b2ee691-471b-44a1-bc6e-90c759868713","format_issues":null,"number":3832} |
1.0.0 | problem:theoremdb-p5638 | problem | theoremdb-p5638 | Clique number of the Paley graph of order 2837 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2837)$ be the graph on $\mathbb{F}_{2837}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2837$. Determine the clique number $\omega(P(2837))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5638",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5638",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5638 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5638",
"url": "https://theoremdb.org/statements/P5638",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5638",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:38+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5638,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.313Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"94ed5339-495d-443d-b01c-2032186847e9","format_issues":null,"number":3833} |
1.0.0 | problem:theoremdb-p5640 | problem | theoremdb-p5640 | Clique number of the Paley graph of order 2857 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2857)$ be the graph on $\mathbb{F}_{2857}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2857$. Determine the clique number $\omega(P(2857))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5640",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5640",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5640 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5640",
"url": "https://theoremdb.org/statements/P5640",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5640",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:44+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5640,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.317Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2056705d-2810-4ef9-b683-f30867fa6751","format_issues":null,"number":3834} |
1.0.0 | problem:theoremdb-p5642 | problem | theoremdb-p5642 | Clique number of the Paley graph of order 2861 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2861)$ be the graph on $\mathbb{F}_{2861}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2861$. Determine the clique number $\omega(P(2861))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5642",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5642",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5642 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5642",
"url": "https://theoremdb.org/statements/P5642",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5642",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:47+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5642,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.322Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f0f50bb2-06d2-40ee-87e0-490e2cfacbbf","format_issues":null,"number":3835} |
1.0.0 | problem:theoremdb-p5644 | problem | theoremdb-p5644 | Clique number of the Paley graph of order 2897 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2897)$ be the graph on $\mathbb{F}_{2897}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2897$. Determine the clique number $\omega(P(2897))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5644",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5644",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5644 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5644",
"url": "https://theoremdb.org/statements/P5644",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5644",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:53+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5644,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.327Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"dc617152-2fa2-4c2c-82f5-6c146287bd37","format_issues":null,"number":3836} |
1.0.0 | problem:theoremdb-p5646 | problem | theoremdb-p5646 | Clique number of the Paley graph of order 2909 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2909)$ be the graph on $\mathbb{F}_{2909}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2909$. Determine the clique number $\omega(P(2909))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5646",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5646",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5646 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5646",
"url": "https://theoremdb.org/statements/P5646",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5646",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:55+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5646,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.331Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"613a7e82-92f6-457b-95e9-dfcd278b8780","format_issues":null,"number":3837} |
1.0.0 | problem:theoremdb-p5648 | problem | theoremdb-p5648 | Clique number of the Paley graph of order 2917 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2917)$ be the graph on $\mathbb{F}_{2917}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2917$. Determine the clique number $\omega(P(2917))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5648",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5648",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5648 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5648",
"url": "https://theoremdb.org/statements/P5648",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5648",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:56+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5648,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.335Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"646f9a85-960d-4672-8b3a-f82d2eaa7bc8","format_issues":null,"number":3838} |
1.0.0 | problem:theoremdb-p5650 | problem | theoremdb-p5650 | Clique number of the Paley graph of order 2953 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2953)$ be the graph on $\mathbb{F}_{2953}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2953$. Determine the clique number $\omega(P(2953))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5650",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5650",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5650 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5650",
"url": "https://theoremdb.org/statements/P5650",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5650",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:57+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5650,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.339Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"9e40f3c6-be24-445b-9ca2-bb8db2367bbc","format_issues":null,"number":3839} |
1.0.0 | problem:theoremdb-p5652 | problem | theoremdb-p5652 | Clique number of the Paley graph of order 2957 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2957)$ be the graph on $\mathbb{F}_{2957}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2957$. Determine the clique number $\omega(P(2957))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5652",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5652",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5652 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5652",
"url": "https://theoremdb.org/statements/P5652",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5652",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:58+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5652,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.344Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b8da22a4-e6be-4049-bbf7-a8c8d443a5f7","format_issues":null,"number":3840} |
1.0.0 | problem:theoremdb-p5654 | problem | theoremdb-p5654 | Clique number of the Paley graph of order 2969 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(2969)$ be the graph on $\mathbb{F}_{2969}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $2969$. Determine the clique number $\omega(P(2969))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5654",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5654",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5654 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5654",
"url": "https://theoremdb.org/statements/P5654",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5654",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:58+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5654,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.349Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f101fede-114d-4980-8e67-0e5a0761aa58","format_issues":null,"number":3841} |
1.0.0 | problem:theoremdb-p5656 | problem | theoremdb-p5656 | Clique number of the Paley graph of order 3001 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3001)$ be the graph on $\mathbb{F}_{3001}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3001$. Determine the clique number $\omega(P(3001))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5656",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5656",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5656 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5656",
"url": "https://theoremdb.org/statements/P5656",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5656",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:44:59+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5656,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.354Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"05b3481e-284b-4917-a6e5-2274ce93a8b8","format_issues":null,"number":3842} |
1.0.0 | problem:theoremdb-p5658 | problem | theoremdb-p5658 | Clique number of the Paley graph of order 3037 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3037)$ be the graph on $\mathbb{F}_{3037}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3037$. Determine the clique number $\omega(P(3037))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5658",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5658",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5658 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5658",
"url": "https://theoremdb.org/statements/P5658",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5658",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:03+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5658,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.358Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"752092a3-8610-40a0-92b5-7f7f9151d361","format_issues":null,"number":3843} |
1.0.0 | problem:theoremdb-p5660 | problem | theoremdb-p5660 | Clique number of the Paley graph of order 3041 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3041)$ be the graph on $\mathbb{F}_{3041}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3041$. Determine the clique number $\omega(P(3041))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5660",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5660",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5660 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5660",
"url": "https://theoremdb.org/statements/P5660",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5660",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:04+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5660,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.362Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"97d398f0-150a-42e2-b308-2cf926ef2dc2","format_issues":null,"number":3844} |
1.0.0 | problem:theoremdb-p5662 | problem | theoremdb-p5662 | Clique number of the Paley graph of order 3049 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3049)$ be the graph on $\mathbb{F}_{3049}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3049$. Determine the clique number $\omega(P(3049))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5662",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5662",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5662 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5662",
"url": "https://theoremdb.org/statements/P5662",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5662",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:05+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5662,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.366Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"acc64e1d-23c7-4915-8770-3d90454bd6ef","format_issues":null,"number":3845} |
1.0.0 | problem:theoremdb-p5664 | problem | theoremdb-p5664 | Clique number of the Paley graph of order 3061 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3061)$ be the graph on $\mathbb{F}_{3061}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3061$. Determine the clique number $\omega(P(3061))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5664",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5664",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5664 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5664",
"url": "https://theoremdb.org/statements/P5664",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5664",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:06+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5664,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.371Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b4a7589a-67de-43a8-9278-86c8f40a10b9","format_issues":null,"number":3846} |
1.0.0 | problem:theoremdb-p5666 | problem | theoremdb-p5666 | Clique number of the Paley graph of order 3089 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3089)$ be the graph on $\mathbb{F}_{3089}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3089$. Determine the clique number $\omega(P(3089))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5666",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5666",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5666 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5666",
"url": "https://theoremdb.org/statements/P5666",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5666",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:07+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5666,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.376Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f768b1bd-91a3-4128-80b9-669222537517","format_issues":null,"number":3847} |
1.0.0 | problem:theoremdb-p5668 | problem | theoremdb-p5668 | Clique number of the Paley graph of order 3109 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3109)$ be the graph on $\mathbb{F}_{3109}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3109$. Determine the clique number $\omega(P(3109))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5668",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5668",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5668 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5668",
"url": "https://theoremdb.org/statements/P5668",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5668",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:07+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5668,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.380Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"b763cbaf-e725-4961-8b41-44bdfafeee29","format_issues":null,"number":3848} |
1.0.0 | problem:theoremdb-p5670 | problem | theoremdb-p5670 | Clique number of the Paley graph of order 3121 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3121)$ be the graph on $\mathbb{F}_{3121}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3121$. Determine the clique number $\omega(P(3121))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5670",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5670",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5670 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5670",
"url": "https://theoremdb.org/statements/P5670",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5670",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:08+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5670,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.385Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3d923bcd-f6c2-4a71-b189-dbf06e57bc72","format_issues":null,"number":3849} |
1.0.0 | problem:theoremdb-p5672 | problem | theoremdb-p5672 | Clique number of the Paley graph of order 3137 | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $P(3137)$ be the graph on $\mathbb{F}_{3137}$ in which distinct vertices $x,y$ are adjacent exactly when $x-y$ is a nonzero quadratic residue modulo $3137$. Determine the clique number $\omega(P(3137))$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5672",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5672",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5672 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5672",
"url": "https://theoremdb.org/statements/P5672",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5672",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:11+00:00","display_standard":{"editorial_review":"submitter_supplied","formal_correspondence":"not_applicable"},"lean_verified":false,"problem_number":5672,"public_status":{"evidence":{"hasFormalization":false,"hasInformalProof":false,"hasRecordedWork":false,"solutionRecord":null},"lean"... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:52.389Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"1c8bfca1-9c59-41e3-a5e2-200568ed6bc9","format_issues":null,"number":3850} |
1.0.0 | problem:theoremdb-p5674 | problem | theoremdb-p5674 | Chromatic number of the circulant graph C(769; 1, 2, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/769\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm14$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5674",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5674",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5674 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5674",
"url": "https://theoremdb.org/statements/P5674",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5674",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:16+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.596Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"d1615d9a-c669-41ae-a20d-f9c6ccec0d6c","format_issues":null,"number":3672} |
1.0.0 | problem:theoremdb-p5676 | problem | theoremdb-p5676 | Chromatic number of the circulant graph C(773; 1, 3, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/773\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm15$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5676",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5676",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5676 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5676",
"url": "https://theoremdb.org/statements/P5676",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5676",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:24+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.601Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"3b23087e-d3e8-43af-84d3-963825f39a0d","format_issues":null,"number":3673} |
1.0.0 | problem:theoremdb-p5678 | problem | theoremdb-p5678 | Chromatic number of the circulant graph C(787; 1, 4, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/787\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm16$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5678",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5678",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5678 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5678",
"url": "https://theoremdb.org/statements/P5678",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5678",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:27+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.605Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"323ff80d-a120-496d-858a-6d059c742db7","format_issues":null,"number":3674} |
1.0.0 | problem:theoremdb-p5680 | problem | theoremdb-p5680 | Chromatic number of the circulant graph C(797; 1, 5, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/797\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm17$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5680",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5680",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5680 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5680",
"url": "https://theoremdb.org/statements/P5680",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5680",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:29+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.610Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"4e1fb01c-32a4-4199-a14d-eccfd6c60aba","format_issues":null,"number":3675} |
1.0.0 | problem:theoremdb-p5682 | problem | theoremdb-p5682 | Chromatic number of the circulant graph C(809; 1, 6, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/809\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm18$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5682",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5682",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5682 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5682",
"url": "https://theoremdb.org/statements/P5682",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5682",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:40+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.614Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"232b0ad9-0f4d-42fe-bf8a-42bed4463edf","format_issues":null,"number":3676} |
1.0.0 | problem:theoremdb-p5684 | problem | theoremdb-p5684 | Chromatic number of the circulant graph C(811; 1, 7, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/811\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm19$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5684",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5684",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5684 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5684",
"url": "https://theoremdb.org/statements/P5684",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5684",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:52+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.618Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"c77c7bb1-b72d-43c5-b270-8fac2954c29b","format_issues":null,"number":3677} |
1.0.0 | problem:theoremdb-p5686 | problem | theoremdb-p5686 | Chromatic number of the circulant graph C(821; 1, 8, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/821\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm20$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5686",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5686",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5686 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5686",
"url": "https://theoremdb.org/statements/P5686",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5686",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:53+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.622Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"707e4fda-c391-429e-b162-f7665e2d9590","format_issues":null,"number":3678} |
1.0.0 | problem:theoremdb-p5688 | problem | theoremdb-p5688 | Chromatic number of the circulant graph C(823; 1, 9, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/823\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm21$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5688",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5688",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5688 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5688",
"url": "https://theoremdb.org/statements/P5688",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5688",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:58+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.626Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"74e6720f-9589-4fdd-b911-c8c6d38a326a","format_issues":null,"number":3679} |
1.0.0 | problem:theoremdb-p5690 | problem | theoremdb-p5690 | Chromatic number of the circulant graph C(827; 1, 10, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/827\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm22$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5690",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5690",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5690 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5690",
"url": "https://theoremdb.org/statements/P5690",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5690",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:58+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.630Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f127ff8d-f0b0-4b35-9bce-0f0cfa581fde","format_issues":null,"number":3680} |
1.0.0 | problem:theoremdb-p5692 | problem | theoremdb-p5692 | Chromatic number of the circulant graph C(829; 1, 11, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/829\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm23$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5692",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5692",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5692 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5692",
"url": "https://theoremdb.org/statements/P5692",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5692",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:45:59+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.635Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"07a0f404-646e-4213-bd33-6ea04669b04f","format_issues":null,"number":3681} |
1.0.0 | problem:theoremdb-p5694 | problem | theoremdb-p5694 | Chromatic number of the circulant graph C(839; 1, 12, 24) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/839\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm24$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5694",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5694",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5694 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5694",
"url": "https://theoremdb.org/statements/P5694",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5694",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:46:02+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.639Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"7738a56f-c3ce-431d-9ff7-d31fa286e27c","format_issues":null,"number":3682} |
1.0.0 | problem:theoremdb-p5696 | problem | theoremdb-p5696 | Chromatic number of the circulant graph C(853; 1, 2, 25) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/853\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm25$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5696",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5696",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5696 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5696",
"url": "https://theoremdb.org/statements/P5696",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5696",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:46:17+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.644Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"2ab5690a-e331-4cb8-bbc9-b648fe58b205","format_issues":null,"number":3683} |
1.0.0 | problem:theoremdb-p5698 | problem | theoremdb-p5698 | Chromatic number of the circulant graph C(857; 1, 3, 26) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/857\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm26$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5698",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5698",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5698 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5698",
"url": "https://theoremdb.org/statements/P5698",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5698",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:46:33+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.649Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"5543e6d6-a842-4b83-a4da-3e7d59faf1b1","format_issues":null,"number":3684} |
1.0.0 | problem:theoremdb-p5700 | problem | theoremdb-p5700 | Chromatic number of the circulant graph C(859; 1, 4, 27) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/859\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm27$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5700",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5700",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5700 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5700",
"url": "https://theoremdb.org/statements/P5700",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5700",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:46:44+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.654Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ac1d0779-66bb-4024-837c-334aa5962d7e","format_issues":null,"number":3685} |
1.0.0 | problem:theoremdb-p5702 | problem | theoremdb-p5702 | Chromatic number of the circulant graph C(863; 1, 5, 28) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/863\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm28$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5702",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5702",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5702 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5702",
"url": "https://theoremdb.org/statements/P5702",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5702",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:47:02+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.659Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f4cba67c-f8b3-4bbe-8ac8-71142dfa81ff","format_issues":null,"number":3686} |
1.0.0 | problem:theoremdb-p5704 | problem | theoremdb-p5704 | Chromatic number of the circulant graph C(877; 1, 6, 29) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/877\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm29$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5704",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5704",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5704 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5704",
"url": "https://theoremdb.org/statements/P5704",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5704",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:47:25+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.663Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6b771a9b-f670-486f-9ebe-f9036d05c908","format_issues":null,"number":3687} |
1.0.0 | problem:theoremdb-p5706 | problem | theoremdb-p5706 | Chromatic number of the circulant graph C(881; 1, 7, 30) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/881\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm7,\pm30$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5706",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5706",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5706 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5706",
"url": "https://theoremdb.org/statements/P5706",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5706",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:47:44+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.667Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"6ff910c8-9f21-4eb3-b6d7-ada03c08e82b","format_issues":null,"number":3688} |
1.0.0 | problem:theoremdb-p5708 | problem | theoremdb-p5708 | Chromatic number of the circulant graph C(883; 1, 8, 14) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/883\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm8,\pm14$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5708",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5708",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5708 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5708",
"url": "https://theoremdb.org/statements/P5708",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5708",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:47:58+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.672Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"bccfad4a-d7d9-4d00-9460-a1e704d1065a","format_issues":null,"number":3689} |
1.0.0 | problem:theoremdb-p5710 | problem | theoremdb-p5710 | Chromatic number of the circulant graph C(887; 1, 9, 15) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/887\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm9,\pm15$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5710",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5710",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5710 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5710",
"url": "https://theoremdb.org/statements/P5710",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5710",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:48:12+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.675Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ebb9d42f-5155-4693-9f70-4d5a4177f871","format_issues":null,"number":3690} |
1.0.0 | problem:theoremdb-p5712 | problem | theoremdb-p5712 | Chromatic number of the circulant graph C(907; 1, 10, 16) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/907\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm10,\pm16$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5712",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5712",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5712 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5712",
"url": "https://theoremdb.org/statements/P5712",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5712",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:48:33+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.680Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"e65800e4-4c27-4e8d-a074-66e7c7b111d7","format_issues":null,"number":3691} |
1.0.0 | problem:theoremdb-p5714 | problem | theoremdb-p5714 | Chromatic number of the circulant graph C(911; 1, 11, 17) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/911\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm11,\pm17$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5714",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5714",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5714 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5714",
"url": "https://theoremdb.org/statements/P5714",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5714",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:48:43+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.684Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"18150aec-40a4-41dc-8e8e-906b169c6e01","format_issues":null,"number":3692} |
1.0.0 | problem:theoremdb-p5716 | problem | theoremdb-p5716 | Chromatic number of the circulant graph C(919; 1, 12, 18) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/919\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm12,\pm18$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5716",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5716",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5716 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5716",
"url": "https://theoremdb.org/statements/P5716",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5716",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:48:59+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.689Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f40ac58f-64be-41e9-adef-a66e5b044bcf","format_issues":null,"number":3693} |
1.0.0 | problem:theoremdb-p5718 | problem | theoremdb-p5718 | Chromatic number of the circulant graph C(929; 1, 2, 19) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/929\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm2,\pm19$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5718",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5718",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5718 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5718",
"url": "https://theoremdb.org/statements/P5718",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5718",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:49:10+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.693Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"ed887b8a-4762-43b4-ba2a-bad354f317b6","format_issues":null,"number":3694} |
1.0.0 | problem:theoremdb-p5720 | problem | theoremdb-p5720 | Chromatic number of the circulant graph C(937; 1, 3, 20) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/937\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm3,\pm20$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5720",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5720",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5720 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5720",
"url": "https://theoremdb.org/statements/P5720",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5720",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:49:25+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.699Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"709d93c7-7c3d-4f98-a624-a867511a67b0","format_issues":null,"number":3695} |
1.0.0 | problem:theoremdb-p5722 | problem | theoremdb-p5722 | Chromatic number of the circulant graph C(941; 1, 4, 21) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/941\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm4,\pm21$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5722",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5722",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5722 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5722",
"url": "https://theoremdb.org/statements/P5722",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5722",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:49:41+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.705Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"db87c8e7-2043-4ea3-a0a5-4998d58f9b9a","format_issues":null,"number":3696} |
1.0.0 | problem:theoremdb-p5724 | problem | theoremdb-p5724 | Chromatic number of the circulant graph C(947; 1, 5, 22) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/947\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm5,\pm22$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5724",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5724",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5724 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5724",
"url": "https://theoremdb.org/statements/P5724",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5724",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:49:55+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.709Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"f835bc4c-b73f-4e09-9aeb-afe8507882fc","format_issues":null,"number":3697} |
1.0.0 | problem:theoremdb-p5726 | problem | theoremdb-p5726 | Chromatic number of the circulant graph C(953; 1, 6, 23) | {
"main": "math",
"sub": "graph theory",
"slug": "graph-theory",
"name": "Graph theory",
"original_discipline": "mathematics"
} | [] | [
{
"code": "05C",
"basis": "community-map",
"evidence": "Inferred from community field: graph-theory"
}
] | Let $H$ have vertex set $\mathbb{Z}/953\mathbb{Z}$, with two vertices adjacent exactly when their difference is congruent to one of $\pm1,\pm6,\pm23$. Determine the chromatic number $\chi(H)$. | open | {
"key": "theoremdb",
"name": "TheoremDB · P5726",
"type": "problem-list",
"url": "https://theoremdb.org/statements/P5726",
"citation": null,
"doi": null,
"arxiv_id": null,
"license": "Selected packets label their content CC0-1.0; original references retain their own terms",
"notes": "Selected problem... | null | null | null | not-recorded | not-recorded | null | [] | [] | TheoremDB P5726 · graph theory | null | Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution. | null | published | incremental | hard | [
"source-curated",
"theoremdb"
] | null | null | null | null | [
{
"kind": "website",
"citation": "TheoremDB P5726",
"url": "https://theoremdb.org/statements/P5726",
"note": null,
"sort_order": 0
}
] | {
"source_record": "P5726",
"imported_at": "2026-09-08",
"status_as_of": "2026-09-08",
"evidence_label": "Source catalogue assessment",
"note": "Full public directory statement. Source lane: curated; source resolution: open. Source verification claims are attributed only; no local Lean verification has been p... | {"created_at":"2026-08-16T08:50:10+00:00","display_standard":{"definitions_format":"typed_textbook_exposition","editorial_review":"submitter_supplied","formal_correspondence":"not_applicable","statement_format":"textbook_mathematics","status":"passed","version":"theoremdb-problem-display-v5"},"lean_verified":false,"pro... | [
"source-full-text-not-present"
] | [] | {
"created_at": "2026-09-08T03:32:15.935Z",
"updated_at": "2026-09-08T03:32:15.935Z",
"published_at": "2026-09-08T03:32:51.714Z",
"solved_at": null
} | 2026-10-10T16:07:49.246Z | {"database_id":"893bc7cd-aaa8-4d4e-ab5b-189f88b6f5bb","format_issues":null,"number":3698} |
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