id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,716 | EP-85 | Erdős Problem #85: Graph Theory, Ramsey Theory | Let $n\geq 4$ and $f(n)$ be minimal such that every graph on $n$ vertices with minimal degree $\geq f(n)$ contains a $C_4$. Is it true that, for all large $n$, $f(n+1)\geq f(n)$? | Erdős Problems (#85, https://www.erdosproblems.com/85). Maintainer status: OPEN. OEIS: A006672. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.85). | 3 | open | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/85",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/85 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,717 | EP-88 | Erdős Problem #88: Graph Theory, Ramsey Theory | For any $\epsilon>0$ there exists $\delta=\delta(\epsilon)>0$ such that if $G$ is a graph on $n$ vertices with no independent set or clique of size $\geq \epsilon\log n$ then $G$ contains an induced subgraph with $m$ edges for all $m\leq \delta n^2$. | Erdős Problems (#88, https://www.erdosproblems.com/88). Maintainer status: PROVED. Erdős prize: $100. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.88). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/88",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/88 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,718 | EP-93 | Erdős Problem #93: Geometry, Convex | If $n$ distinct points in $\mathbb{R}^2$ form a convex polygon then they determine at least $\lfloor \frac{n}{2}\rfloor$ distinct distances. | Erdős Problems (#93, https://www.erdosproblems.com/93). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.93). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/93",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"convex",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/93 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,719 | EP-94 | Erdős Problem #94: Geometry, Convex | Suppose $n$ points in $\mathbb{R}^2$ determine a convex polygon and the set of distances between them is $\{u_1,\ldots,u_t\}$. Suppose $u_i$ appears as the distance between $f(u_i)$ many pairs of points. Then\[\sum_i f(u_i)^2 \ll n^3.\] | Erdős Problems (#94, https://www.erdosproblems.com/94). Maintainer status: PROVED (LEAN). Erdős prize: £25. OEIS: A387858. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.94). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/94",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"convex",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/94 | Erdős Problems (erdosproblems.com) | £25 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,720 | EP-95 | Erdős Problem #95: Geometry, Convex | Let $x_1,\ldots,x_n\in\mathbb{R}^2$ determine the set of distances $\{u_1,\ldots,u_t\}$. Suppose $u_i$ appears as the distance between $f(u_i)$ many pairs of points. Then for all $\epsilon>0$\[\sum_i f(u_i)^2 \ll_\epsilon n^{3+\epsilon}.\] | Erdős Problems (#95, https://www.erdosproblems.com/95). Maintainer status: PROVED (LEAN). Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.95). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/95",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"convex",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/95 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,721 | EP-97 | Erdős Problem #97: Geometry, Distances | Does every convex polygon have a vertex with no other $4$ vertices equidistant from it? | Erdős Problems (#97, https://www.erdosproblems.com/97). Maintainer status: FALSIFIABLE. Erdős prize: $100. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.97). | 3 | open | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/97",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances",
"convex"
] | null | null | null | null | https://www.erdosproblems.com/97 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,722 | EP-105 | Erdős Problem #105: Geometry | Let $A,B\subset \mathbb{R}^2$ be disjoint sets of size $n$ and $n-3$ respectively, with not all of $A$ contained on a single line. Is there a line which contains at least two points from $A$ and no points from $B$? | Erdős Problems (#105, https://www.erdosproblems.com/105). Maintainer status: DISPROVED (LEAN). Erdős prize: $50. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.105). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/105",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/105 | Erdős Problems (erdosproblems.com) | $50 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,723 | EP-106 | Erdős Problem #106: Geometry | Draw $n$ squares inside the unit square with no common interior point. Let $f(n)$ be the maximum possible sum of the side-lengths of the squares. Is $f(k^2+1)=k$? | Erdős Problems (#106, https://www.erdosproblems.com/106). Maintainer status: DISPROVED (LEAN). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/106",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/106 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,724 | EP-107 | Erdős Problem #107: Geometry, Convex | Let $f(n)$ be minimal such that any $f(n)$ points in $\mathbb{R}^2$, no three on a line, contain $n$ points which form the vertices of a convex $n$-gon. Prove that $f(n)=2^{n-2}+1$. | Erdős Problems (#107, https://www.erdosproblems.com/107). Maintainer status: FALSIFIABLE. Erdős prize: $500. 'Happy Ending' problem OEIS: A000051. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.107). | 3 | open | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | [
"GEO-035",
"GEOM-020"
] | {
"source_url": "https://www.erdosproblems.com/107",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | 'Happy Ending' problem | [
"erdos-problems",
"geometry",
"convex"
] | null | null | null | null | https://www.erdosproblems.com/107 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,725 | EP-109 | Erdős Problem #109: Additive Combinatorics | Any $A\subseteq \mathbb{N}$ of positive upper density contains a sumset $B+C$ where both $B$ and $C$ are infinite. | Erdős Problems (#109, https://www.erdosproblems.com/109). Maintainer status: PROVED (LEAN). Erdős sumset conjecture Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.109). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/109",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | Erdős sumset conjecture | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/109 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,726 | EP-110 | Erdős Problem #110: Graph Theory, Chromatic Number | Is there some $F(n)$ such that every graph with chromatic number $\aleph_1$ has, for all large $n$, a subgraph with chromatic number $n$ on at most $F(n)$ vertices? | Erdős Problems (#110, https://www.erdosproblems.com/110). Maintainer status: DISPROVED. | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/110",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number",
"cycles"
] | null | null | null | null | https://www.erdosproblems.com/110 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,727 | EP-113 | Erdős Problem #113: Graph Theory, Turan Number | If $G$ is bipartite then $\mathrm{ex}(n;G)\ll n^{3/2}$ if and only $G$ is $2$-degenerate, that is, $G$ contains no induced subgraph with minimal degree at least 3. | Erdős Problems (#113, https://www.erdosproblems.com/113). Maintainer status: DISPROVED (LEAN). Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.113). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/113",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"turan-number"
] | null | null | null | null | https://www.erdosproblems.com/113 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,728 | EP-115 | Erdős Problem #115: Polynomials, Analysis | If $p(z)$ is a polynomial of degree $n$ such that $\{z: \lvert p(z)\rvert\leq 1\}$ is connected then is it true that\[\max_{\substack{z\in\mathbb{C}\\ \lvert p(z)\rvert\leq 1}} \lvert p'(z)\rvert \leq (\tfrac{1}{2}+o(1))n^2?\] | Erdős Problems (#115, https://www.erdosproblems.com/115). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.115). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/115",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"polynomials",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/115 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,729 | EP-116 | Erdős Problem #116: Polynomials, Analysis | Let $p(z)=\prod_{i=1}^n (z-z_i)$ for $\lvert z_i\rvert \leq 1$. Is it true that\[\lvert\{ z: \lvert p(z)\rvert <1\}\rvert>n^{-O(1)}\](or perhaps even $>(\log n)^{-O(1)}$)? | Erdős Problems (#116, https://www.erdosproblems.com/116). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.116). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/116",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"polynomials",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/116 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,730 | EP-118 | Erdős Problem #118: Set Theory, Ramsey Theory | Let $\alpha$ be a cardinal or ordinal number or an order type such that every two-colouring of $K_\alpha$ contains either a red $K_\alpha$ or a blue $K_3$. For every $n\geq 3$ must every two-colouring of $K_\alpha$ contain either a red $K_\alpha$ or a blue $K_n$? | Erdős Problems (#118, https://www.erdosproblems.com/118). Maintainer status: DISPROVED. | 3 | solved | Paul Erdős | null | 10 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/118",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"set-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/118 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,731 | EP-121 | Erdős Problem #121: Number Theory, Squares | Let $F_{k}(N)$ be the size of the largest $A\subseteq \{1,\ldots,N\}$ such that the product of no $k$ many distinct elements of $A$ is a square. Is $F_5(N)=(1-o(1))N$? More generally, is $F_{2k+1}(N)=(1-o(1))N$? | Erdős Problems (#121, https://www.erdosproblems.com/121). Maintainer status: DISPROVED (LEAN). OEIS: A028391, A013928, A372306, A373319, A373178, A360659, A373114, A143301. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.121). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/121",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"squares"
] | null | null | null | null | https://www.erdosproblems.com/121 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,732 | EP-127 | Erdős Problem #127: Is there an infinite sequence of $m_i$ such that $f(m_i)\to \infty$? | Let $f(m)$ be maximal such that every graph with $m$ edges must contain a bipartite graph with\[\geq \frac{m}{2}+\frac{\sqrt{8m+1}-1}{8}+f(m)\]edges. Is there an infinite sequence of $m_i$ such that $f(m_i)\to \infty$? | Erdős Problems (#127, https://www.erdosproblems.com/127). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.127). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/127",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/127 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,733 | EP-128 | Erdős Problem #128: Must $G$ contain a triangle? | Let $G$ be a graph with $n$ vertices such that every induced subgraph on $\geq \lfloor n/2\rfloor$ vertices has more than $n^2/50$ edges. Must $G$ contain a triangle? | Erdős Problems (#128, https://www.erdosproblems.com/128). Maintainer status: FALSIFIABLE. Erdős prize: $250. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.128). | 3 | open | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/128",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/128 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,734 | EP-133 | Erdős Problem #133: | Let $f(n)$ be minimal such that every triangle-free graph $G$ with $n$ vertices and diameter $2$ contains a vertex with degree $\geq f(n)$.
What is the order of growth of $f(n)$? Does $f(n)/\sqrt{n}\to \infty$? | Erdős Problems (#133, https://www.erdosproblems.com/133). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.133). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/133",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/133 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,735 | EP-134 | Erdős Problem #134: Graph Theory | Let $\epsilon,\delta>0$ and $n$ be sufficiently large in terms of $\epsilon$ and $\delta$. Let $G$ be a triangle-free graph on $n$ vertices with maximum degree $<n^{1/2-\epsilon}$.
Can $G$ be made into a triangle-free graph with diameter $2$ by adding at most $\delta n^2$ edges? | Erdős Problems (#134, https://www.erdosproblems.com/134). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.134). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/134",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/134 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,736 | EP-135 | Erdős Problem #135: Must $A$ determine $\gg n^2$ many distances? | Let $A\subset \mathbb{R}^2$ be a set of $n$ points such that any subset of size $4$ determines at least $5$ distinct distances. Must $A$ determine $\gg n^2$ many distances? | Erdős Problems (#135, https://www.erdosproblems.com/135). Maintainer status: DISPROVED (LEAN). Erdős prize: $250. | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/135",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"distances",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/135 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,737 | EP-136 | Erdős Problem #136: Determine the size of $f(n)$ | Let $f(n)$ be the smallest number of colours required to colour the edges of $K_n$ such that every $K_4$ contains at least 5 colours. Determine the size of $f(n)$. | Erdős Problems (#136, https://www.erdosproblems.com/136). Maintainer status: SOLVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.136). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/136",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/136 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,738 | EP-139 | Erdős Problem #139: Additive Combinatorics, Arithmetic Progressions | Let $r_k(N)$ be the size of the largest subset of $\{1,\ldots,N\}$ which does not contain a non-trivial $k$-term arithmetic progression. Prove that $r_k(N)=o(N)$. | Erdős Problems (#139, https://www.erdosproblems.com/139). Maintainer status: PROVED (LEAN). Erdős prize: $1000. Szemerédi's theorem OEIS: A003002, A003003, A003004, A003005. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.139). | 4 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/139",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | Szemerédi's theorem | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/139 | Erdős Problems (erdosproblems.com) | $1000 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,739 | EP-140 | Erdős Problem #140: Additive Combinatorics, Arithmetic Progressions | Let $r_3(N)$ be the size of the largest subset of $\{1,\ldots,N\}$ which does not contain a non-trivial $3$-term arithmetic progression. Prove that $r_3(N)\ll N/(\log N)^C$ for every $C>0$. | Erdős Problems (#140, https://www.erdosproblems.com/140). Maintainer status: PROVED (LEAN). Erdős prize: $500. OEIS: A003002. | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/140",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/140 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,740 | EP-144 | Erdős Problem #144: Number Theory, Divisors | The density of integers which have two divisors $d_1,d_2$ such that $d_1<d_2<2d_1$ exists and is equal to $1$. | Erdős Problems (#144, https://www.erdosproblems.com/144). Maintainer status: PROVED (LEAN). Erdős prize: $250. OEIS: A005279. | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/144",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"divisors"
] | null | null | null | null | https://www.erdosproblems.com/144 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,741 | EP-147 | Erdős Problem #147: Graph Theory, Turan Number | If $H$ is bipartite with minimum degree $r$ then there exists $\epsilon=\epsilon(H)>0$ such that\[\mathrm{ex}(n;H) \gg n^{2-\frac{1}{r-1}+\epsilon}.\] | Erdős Problems (#147, https://www.erdosproblems.com/147). Maintainer status: DISPROVED (LEAN). Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.147). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/147",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"turan-number"
] | null | null | null | null | https://www.erdosproblems.com/147 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,742 | EP-150 | Erdős Problem #150: Graph Theory | A minimal cut of a graph is a minimal set of vertices whose removal disconnects the graph. Let $c(n)$ be the maximum number of minimal cuts a graph on $n$ vertices can have.
Does $c(n)^{1/n}\to \alpha$ for some $\alpha <2$? | Erdős Problems (#150, https://www.erdosproblems.com/150). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.150). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/150",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/150 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,743 | EP-154 | Erdős Problem #154: Sidon Sets | Let $A\subset \{1,\ldots,N\}$ be a Sidon set with $\lvert A\rvert\sim N^{1/2}$. Must $A+A$ be well-distributed over all small moduli? In particular, must about half the elements of $A+A$ be even and half odd? | Erdős Problems (#154, https://www.erdosproblems.com/154). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.154). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/154",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/154 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,744 | EP-157 | Erdős Problem #157: Does there exist an infinite Sidon set which is an asymptotic basis of order 3? | Does there exist an infinite Sidon set which is an asymptotic basis of order 3? | Erdős Problems (#157, https://www.erdosproblems.com/157). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.157). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/157",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/157 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,745 | EP-163 | Erdős Problem #163: Graph Theory, Ramsey Theory | For any $d\geq 1$ if $H$ is a graph such that every subgraph contains a vertex of degree at most $d$ then $R(H)\ll_d n$. | Erdős Problems (#163, https://www.erdosproblems.com/163). Maintainer status: PROVED. Burr-Erdős conjecture Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.163). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/163",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | Burr-Erdős conjecture | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/163 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,746 | EP-164 | Erdős Problem #164: Number Theory, Primitive Sets | A set $A\subset \mathbb{N}$ is primitive if no member of $A$ divides another. Is the sum\[\sum_{n\in A}\frac{1}{n\log n}\]maximised over all primitive sets when $A$ is the set of primes? | Erdős Problems (#164, https://www.erdosproblems.com/164). Maintainer status: PROVED (LEAN). OEIS: A137245. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.164). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/164",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primitive-sets"
] | null | null | null | null | https://www.erdosproblems.com/164 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,747 | EP-166 | Erdős Problem #166: Prove that\[R(4,k) \gg \frac{k^3}{(\log k)^{O(1)}}.\] | Prove that\[R(4,k) \gg \frac{k^3}{(\log k)^{O(1)}}.\] | Erdős Problems (#166, https://www.erdosproblems.com/166). Maintainer status: PROVED. Erdős prize: $250. OEIS: A059442. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.166). | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/166",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/166 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,748 | EP-167 | Erdős Problem #167: Graph Theory | If $G$ is a graph with at most $k$ edge disjoint triangles then can $G$ be made triangle-free after removing at most $2k$ edges? | Erdős Problems (#167, https://www.erdosproblems.com/167). Maintainer status: FALSIFIABLE. | 3 | open | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/167",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/167 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,749 | EP-171 | Erdős Problem #171: Additive Combinatorics, Combinatorics | Is it true that for every $\epsilon>0$ and integer $t\geq 1$, if $N$ is sufficiently large and $A$ is a subset of $[t]^N$ of size at least $\epsilon t^N$ then $A$ must contain a combinatorial line $P$ (a set $P=\{p_1,\ldots,p_t\}$ where for each coordinate $1\leq j\leq t$ the $j$th coordinate of $p_i$ is either $i$ or ... | Erdős Problems (#171, https://www.erdosproblems.com/171). Maintainer status: PROVED (LEAN). density Hales-Jewett OEIS: A156989. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.171). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/171",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | density Hales-Jewett | [
"erdos-problems",
"additive-combinatorics",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/171 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,750 | EP-175 | Erdős Problem #175: Number Theory, Binomial Coefficients | Show that, for any $n\geq 5$, the binomial coefficient $\binom{2n}{n}$ is not squarefree. | Erdős Problems (#175, https://www.erdosproblems.com/175). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.175). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/175",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"binomial-coefficients"
] | null | null | null | null | https://www.erdosproblems.com/175 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,751 | EP-178 | Erdős Problem #178: Discrepancy | Let $A_1,A_2,\ldots$ be an infinite collection of infinite sets of integers, say $A_i=\{a_{i1}<a_{i2}<\cdots\}$. Does there exist some $f:\mathbb{N}\to\{-1,1\}$ such that\[\max_{m, 1\leq i\leq d} \left\lvert \sum_{1\leq j\leq m} f(a_{ij})\right\rvert \ll_d 1\]for all $d\geq 1$? | Erdős Problems (#178, https://www.erdosproblems.com/178). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.178). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/178",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"discrepancy"
] | null | null | null | null | https://www.erdosproblems.com/178 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,752 | EP-179 | Erdős Problem #179: Additive Combinatorics, Arithmetic Progressions | Let $1\leq k<\ell$ be integers and define $F_k(N,\ell)$ to be minimal such that every set $A\subset \mathbb{N}$ of size $N$ which contains at least $F_k(N,\ell)$ many $k$-term arithmetic progressions must contain an $\ell$-term arithmetic progression. Find good upper bounds for $F_k(N,\ell)$. Is it true that\[F_3(N,4)=... | Erdős Problems (#179, https://www.erdosproblems.com/179). Maintainer status: PROVED. | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/179",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/179 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,753 | EP-182 | Erdős Problem #182: Graph Theory | Let $k\geq 3$. What is the maximum number of edges that a graph on $n$ vertices can contain if it does not have a $k$-regular subgraph? Is it $\ll n^{1+o(1)}$? | Erdős Problems (#182, https://www.erdosproblems.com/182). Maintainer status: PROVED. | 3 | solved | Paul Erdős | null | 3 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/182",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/182 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,754 | EP-185 | Erdős Problem #185: 1,2\}^n$ which contains no three points on a line. Is it true that $f_3(n)=o(3^n)$? | Let $f_3(n)$ be the maximal size of a subset of $\{0,1,2\}^n$ which contains no three points on a line. Is it true that $f_3(n)=o(3^n)$? | Erdős Problems (#185, https://www.erdosproblems.com/185). Maintainer status: PROVED (LEAN). OEIS: A003142. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.185). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/185",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/185 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,755 | EP-186 | Erdős Problem #186: Additive Combinatorics | Let $F(N)$ be the maximal size of $A\subseteq \{1,\ldots,N\}$ which is 'non-averaging', so that no $n\in A$ is the arithmetic mean of at least two elements in $A$. What is the order of growth of $F(N)$? | Erdős Problems (#186, https://www.erdosproblems.com/186). Maintainer status: SOLVED. OEIS: A389784. | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/186",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/186 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,756 | EP-189 | Erdős Problem #189: Geometry, Ramsey Theory | If $\mathbb{R}^2$ is finitely coloured then must there exist some colour class which contains the vertices of a rectangle of every area? | Erdős Problems (#189, https://www.erdosproblems.com/189). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.189). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/189",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/189 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,757 | EP-191 | Erdős Problem #191: Combinatorics, Ramsey Theory | Let $C>0$ be arbitrary. Is it true that, if $n$ is sufficiently large depending on $C$, then in any $2$-colouring of $\binom{\{2,\ldots,n\}}{2}$ there exists some $X\subseteq \{2,\ldots,n\}$ such that $\binom{X}{2}$ is monochromatic and\[\sum_{x\in X}\frac{1}{\log x}\geq C?\] | Erdős Problems (#191, https://www.erdosproblems.com/191). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.191). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/191",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"combinatorics",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/191 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,758 | EP-192 | Erdős Problem #192: Arithmetic Progressions, Combinatorics | Let $A=\{a_1,a_2,\ldots\}\subset \mathbb{R}^d$ be an infinite sequence such that $a_{i+1}-a_i$ is a positive unit vector (i.e. is of the form $(0,0,\ldots,1,0,\ldots,0)$). For which $d$ must $A$ contain a three-term arithmetic progression? | Erdős Problems (#192, https://www.erdosproblems.com/192). Maintainer status: SOLVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.192). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/192",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"arithmetic-progressions",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/192 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,759 | EP-194 | Erdős Problem #194: Arithmetic Progressions | Let $k\geq 3$. Must any ordering of $\mathbb{R}$ contain a monotone $k$-term arithmetic progression, that is, some $x_1<\cdots<x_k$ which forms an increasing or decreasing $k$-term arithmetic progression? | Erdős Problems (#194, https://www.erdosproblems.com/194). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.194). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/194",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/194 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,760 | EP-198 | Erdős Problem #198: Additive Combinatorics, Sidon Sets | If $A\subset \mathbb{N}$ is a Sidon set then must the complement of $A$ contain an infinite arithmetic progression? | Erdős Problems (#198, https://www.erdosproblems.com/198). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.198). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/198",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"sidon-sets",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/198 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,761 | EP-199 | Erdős Problem #199: Arithmetic Progressions | If $A\subset \mathbb{R}$ does not contain a 3-term arithmetic progression then must $\mathbb{R}\backslash A$ contain an infinite arithmetic progression? | Erdős Problems (#199, https://www.erdosproblems.com/199). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.199). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/199",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/199 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,762 | EP-204 | Erdős Problem #204: Covering Systems, Divisors | Are there $n$ such that there is a covering system with moduli the divisors of $n$ which is 'as disjoint as possible'?
That is, for all $d\mid n$ with $d>1$ there is an associated $a_d$ such that every integer is congruent to some $a_d\pmod{d}$, and if there is some integer $x$ with\[x\equiv a_d\pmod{d}\textrm{ and }x... | Erdős Problems (#204, https://www.erdosproblems.com/204). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.204). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/204",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"covering-systems",
"divisors"
] | null | null | null | null | https://www.erdosproblems.com/204 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,763 | EP-205 | Erdős Problem #205: Number Theory | Is it true that all sufficiently large $n$ can be written as $2^k+m$ for some $k\geq 0$, where $\Omega(m)<\log\log m$? (Here $\Omega(m)$ is the number of prime divisors of $m$ counted with multiplicity.) What about $<\epsilon \log\log m$? Or some more slowly growing function? | Erdős Problems (#205, https://www.erdosproblems.com/205). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.205). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/205",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/205 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,764 | EP-206 | Erdős Problem #206: Number Theory, Unit Fractions | Let $x>0$ be a real number. For any $n\geq 1$ let\[R_n(x) = \sum_{i=1}^n\frac{1}{m_i}<x\]be the maximal sum of $n$ distinct unit fractions which is $<x$.
Is it true that, for almost all $x$, for sufficiently large $n$, we have\[R_{n+1}(x)=R_n(x)+\frac{1}{m},\]where $m$ is minimal such that $m$ does not appear in $R_n(... | Erdős Problems (#206, https://www.erdosproblems.com/206). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.206). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/206",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/206 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,765 | EP-207 | Erdős Problem #207: Combinatorics, Hypergraphs | For any $g\geq 2$, if $n$ is sufficiently large and $\equiv 1,3\pmod{6}$ then there exists a 3-uniform hypergraph on $n$ vertices such that
- every pair of vertices is contained in exactly one edge (i.e. the graph is a Steiner triple system) and
- for any $2\leq j\leq g$ any collection of $j$ edges contains at least ... | Erdős Problems (#207, https://www.erdosproblems.com/207). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.207). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/207",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"combinatorics",
"hypergraphs"
] | null | null | null | null | https://www.erdosproblems.com/207 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,766 | EP-209 | Erdős Problem #209: Geometry | Let $A$ be a finite collection of $d\geq 4$ non-parallel lines in $\mathbb{R}^2$ such that there are no points where at least four lines from $A$ meet. Must there exist a 'Gallai triangle' (or 'ordinary triangle'): three lines from $A$ which intersect in three points, and each of these intersection points only intersec... | Erdős Problems (#209, https://www.erdosproblems.com/209). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.209). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/209",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/209 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,767 | EP-210 | Erdős Problem #210: Geometry | Let $f(n)$ be minimal such that the following holds. For any $n$ points in $\mathbb{R}^2$, not all on a line, there must be at least $f(n)$ many lines which contain exactly 2 points (called 'ordinary lines'). Does $f(n)\to \infty$? How fast? | Erdős Problems (#210, https://www.erdosproblems.com/210). Maintainer status: PROVED. OEIS: A003034. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.210). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/210",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/210 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,768 | EP-211 | Erdős Problem #211: Geometry | Let $1\leq k<n$. Given $n$ points in $\mathbb{R}^2$, at most $n-k$ on any line, there are $\gg kn$ many lines which contain at least two points. | Erdős Problems (#211, https://www.erdosproblems.com/211). Maintainer status: PROVED. Erdős prize: $100. | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/211",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/211 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,769 | EP-214 | Erdős Problem #214: Must the complement of $S$ contain four points which form a unit square? | Let $S\subset \mathbb{R}^2$ be such that no two points in $S$ are distance $1$ apart. Must the complement of $S$ contain four points which form a unit square? | Erdős Problems (#214, https://www.erdosproblems.com/214). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.214). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/214",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/214 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,770 | EP-215 | Erdős Problem #215: Geometry | Does there exist $S\subseteq \mathbb{R}^2$ such that every set congruent to $S$ (that is, $S$ after some translation and rotation) contains exactly one point from $\mathbb{Z}^2$? | Erdős Problems (#215, https://www.erdosproblems.com/215). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.215). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/215",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/215 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,771 | EP-216 | Erdős Problem #216: e. with no point in the interior). Does $g(k)$ exist? If so, estimate $g(k)$ | Let $g(k)$ be the smallest integer (if any such exists) such that any $g(k)$ points in $\mathbb{R}^2$ contains an empty convex $k$-gon (i.e. with no point in the interior). Does $g(k)$ exist? If so, estimate $g(k)$. | Erdős Problems (#216, https://www.erdosproblems.com/216). Maintainer status: DISPROVED. OEIS: A381776. | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/216",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"convex"
] | null | null | null | null | https://www.erdosproblems.com/216 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,772 | EP-219 | Erdős Problem #219: Are there arbitrarily long arithmetic progressions of primes? | Are there arbitrarily long arithmetic progressions of primes? | Erdős Problems (#219, https://www.erdosproblems.com/219). Maintainer status: PROVED (LEAN). Green-Tao theorem OEIS: A005115, A113827, A123556. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.219). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/219",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | Green-Tao theorem | [
"erdos-problems",
"number-theory",
"additive-combinatorics",
"primes",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/219 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,773 | EP-220 | Erdős Problem #220: Number Theory | Let $n\geq 1$ and\[A=\{a_1<\cdots <a_{\phi(n)}\}=\{ 1\leq m<n: (m,n)=1\}.\]Is it true that\[ \sum_{1\leq k<\phi(n)}(a_{k+1}-a_k)^2 \ll \frac{n^2}{\phi(n)}?\] | Erdős Problems (#220, https://www.erdosproblems.com/220). Maintainer status: PROVED (LEAN). Erdős prize: $500. OEIS: A322144. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.220). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/220",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/220 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,774 | EP-221 | Erdős Problem #221: Number Theory, Additive Basis | Is there a set $A\subset\mathbb{N}$ such that, for all large $N$,\[\lvert A\cap\{1,\ldots,N\}\rvert \ll N/\log N\]and such that every large integer can be written as $2^k+a$ for some $k\geq 0$ and $a\in A$? | Erdős Problems (#221, https://www.erdosproblems.com/221). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.221). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/221",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/221 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,775 | EP-223 | Erdős Problem #223: Geometry, Distances | Let $d\geq 2$ and $n\geq 2$. Let $f_d(n)$ be maximal such that there exists some set of $n$ points $A\subseteq \mathbb{R}^d$, with diameter $1$, in which the distance 1 occurs between $f_d(n)$ many pairs of points in $A$. Estimate $f_d(n)$. | Erdős Problems (#223, https://www.erdosproblems.com/223). Maintainer status: SOLVED. OEIS: A008811. | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/223",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/223 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,776 | EP-224 | Erdős Problem #224: Geometry | If $A\subseteq \mathbb{R}^d$ is any set of $2^d+1$ points then some three points in $A$ determine an obtuse angle. | Erdős Problems (#224, https://www.erdosproblems.com/224). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.224). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/224",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/224 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,777 | EP-225 | Erdős Problem #225: Analysis | Let\[ f(\theta) = \sum_{0\leq k\leq n}c_k e^{ik\theta}\]be a trigonometric polynomial all of whose roots are real, such that $\max_{\theta\in [0,2\pi]}\lvert f(\theta)\rvert=1$. Then\[\int_0^{2\pi}\lvert f(\theta)\rvert \mathrm{d}\theta \leq 4.\] | Erdős Problems (#225, https://www.erdosproblems.com/225). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.225). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/225",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/225 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,778 | EP-226 | Erdős Problem #226: Analysis | Is there an entire non-linear function $f$ such that, for all $x\in\mathbb{R}$, $x$ is rational if and only if $f(x)$ is? | Erdős Problems (#226, https://www.erdosproblems.com/226). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.226). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/226",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/226 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,779 | EP-227 | Erdős Problem #227: Analysis | Let $f=\sum_{n=0}^\infty a_nz^n$ be an entire function which is not a polynomial. Is it true that if\[\lim_{r\to \infty} \frac{\max_n\lvert a_nr^n\rvert}{\max_{\lvert z\rvert=r}\lvert f(z)\rvert}\]exists then it must be $0$? | Erdős Problems (#227, https://www.erdosproblems.com/227). Maintainer status: DISPROVED. | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/227",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/227 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,780 | EP-228 | Erdős Problem #228: Analysis, Polynomials | Does there exist, for all large $n$, a polynomial $P$ of degree $n$, with coefficients $\pm 1$, such that\[\sqrt{n} \ll \lvert P(z) \rvert \ll \sqrt{n}\]for all $\lvert z\rvert =1$, with the implied constants independent of $z$ and $n$? | Erdős Problems (#228, https://www.erdosproblems.com/228). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.228). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/228",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"polynomials"
] | null | null | null | null | https://www.erdosproblems.com/228 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,781 | EP-229 | Erdős Problem #229: Analysis, Iterated Functions | Let $(S_n)_{n\geq 1}$ be a sequence of sets of complex numbers, none of which have a finite limit point. Does there exist an entire transcendental function $f(z)$ such that, for all $n\geq 1$, there exists some $k_n\geq 0$ such that\[f^{(k_n)}(z) = 0\textrm{ for all }z\in S_n?\] | Erdős Problems (#229, https://www.erdosproblems.com/229). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.229). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/229",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"iterated-functions"
] | null | null | null | null | https://www.erdosproblems.com/229 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,782 | EP-230 | Erdős Problem #230: Analysis, Polynomials | Let $P(z)=\sum_{1\leq k\leq n}a_kz^k$ for some $a_k\in \mathbb{C}$ with $\lvert a_k\rvert=1$ for $1\leq k\leq n$. Does there exist a constant $c>0$ such that, for $n\geq 2$, we have\[\max_{\lvert z\rvert=1}\lvert P(z)\rvert \geq (1+c)\sqrt{n}?\] | Erdős Problems (#230, https://www.erdosproblems.com/230). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.230). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/230",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"polynomials"
] | null | null | null | null | https://www.erdosproblems.com/230 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,783 | EP-231 | Erdős Problem #231: Combinatorics | Let $S$ be a string of length $2^k-1$ formed from an alphabet of $k$ characters. Must $S$ contain an abelian square: two consecutive blocks $x$ and $y$ such that $y$ is a permutation of $x$? | Erdős Problems (#231, https://www.erdosproblems.com/231). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.231). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/231",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/231 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,784 | EP-232 | Erdős Problem #232: Geometry, Distances | For $A\subset \mathbb{R}^2$ we define the upper density as\[\overline{\delta}(A)=\limsup_{R\to \infty}\frac{\lambda(A \cap B_R)}{\lambda(B_R)},\]where $\lambda$ is the Lebesgue measure and $B_R$ is the ball of radius $R$.
Estimate\[m_1=\sup \overline{\delta}(A),\]where $A$ ranges over all measurable subsets of $\mathb... | Erdős Problems (#232, https://www.erdosproblems.com/232). Maintainer status: PROVED. | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/232",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/232 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,785 | EP-235 | Erdős Problem #235: Number Theory | Let $N_k=2\cdot 3\cdots p_k$ and $\{a_1<a_2<\cdots <a_{\phi(N_k)}\}$ be the integers $<N_k$ which are relatively prime to $N_k$. Then, for any $c\geq 0$, the limit\[\frac{\#\{ a_i-a_{i-1}\leq c \frac{N_k}{\phi(N_k)}: 2\leq i\leq \phi(N_k)\}}{\phi(N_k)}\]exists and is a continuous function of $c$. | Erdős Problems (#235, https://www.erdosproblems.com/235). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.235). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/235",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/235 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,786 | EP-237 | Erdős Problem #237: Number Theory, Primes | Let $A\subseteq \mathbb{N}$ be a set such that $\lvert A\cap \{1,\ldots,N\}\rvert \gg \log N$ for all large $N$. Let $f(n)$ count the number of solutions to $n=p+a$ for $p$ prime and $a\in A$. Is it true that $\limsup f(n)=\infty$? | Erdős Problems (#237, https://www.erdosproblems.com/237). Maintainer status: PROVED (LEAN). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/237",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/237 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,787 | EP-239 | Erdős Problem #239: Is it true that\[ \lim_{N\to \infty}\frac{1}{N}\sum_{n\leq N}f(n)\]always exists? | Let $f:\mathbb{N}\to \{-1,1\}$ be a multiplicative function. Is it true that\[ \lim_{N\to \infty}\frac{1}{N}\sum_{n\leq N}f(n)\]always exists? | Erdős Problems (#239, https://www.erdosproblems.com/239). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.239). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/239",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/239 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,788 | EP-240 | Erdős Problem #240: Number Theory, Primes | Is there an infinite set of primes $P$ such that if $\{a_1<a_2<\cdots\}$ is the set of integers divisible only by primes in $P$ then $\lim a_{i+1}-a_i=\infty$? | Erdős Problems (#240, https://www.erdosproblems.com/240). Maintainer status: PROVED. | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/240",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/240 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,789 | EP-242 | Erdős Problem #242: Number Theory, Unit Fractions | For every $n>2$ there exist distinct integers $1\leq x<y<z$ such that\[\frac{4}{n} = \frac{1}{x}+\frac{1}{y}+\frac{1}{z}.\] | Erdős Problems (#242, https://www.erdosproblems.com/242). Maintainer status: FALSIFIABLE. Erdős-Straus conjecture OEIS: A073101, A075245, A075246, A075247, A075248, A287116. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.242). | 3 | open | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | [
"NT-012",
"NT-024",
"OPG-37397"
] | {
"source_url": "https://www.erdosproblems.com/242",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | Erdős-Straus conjecture | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/242 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,790 | EP-245 | Erdős Problem #245: Additive Combinatorics | Let $A\subseteq \mathbb{N}$ be an infinite set such that $\lvert A\cap \{1,\ldots,N\}\rvert=o(N)$. Is it true that\[\limsup_{N\to \infty}\frac{\lvert (A+A)\cap \{1,\ldots,N\}\rvert}{\lvert A\cap \{1,\ldots,N\}\rvert}\geq 3?\] | Erdős Problems (#245, https://www.erdosproblems.com/245). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.245). | 3 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/245",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/245 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,791 | EP-246 | Erdős Problem #246: Number Theory | Let $(a,b)=1$. The set $\{a^kb^l: k,l\geq 0\}$ is complete - that is, every large integer is the sum of distinct integers of the form $a^kb^l$ with $k,l\geq 0$. | Erdős Problems (#246, https://www.erdosproblems.com/246). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.246). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/246",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/246 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,792 | EP-248 | Erdős Problem #248: Number Theory | Are there infinitely many $n$ such that, for all $k\geq 1$,\[ \omega(n+k) \ll k?\](Here $\omega(n)$ is the number of distinct prime divisors of $n$.) | Erdős Problems (#248, https://www.erdosproblems.com/248). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.248). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/248",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/248 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,793 | EP-250 | Erdős Problem #250: Number Theory, Irrationality | Is\[\sum \frac{\sigma(n)}{2^n}\]irrational? (Here $\sigma(n)$ is the sum of divisors function.) | Erdős Problems (#250, https://www.erdosproblems.com/250). Maintainer status: PROVED (LEAN). OEIS: A066766. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.250). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/250",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/250 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,794 | EP-253 | Erdős Problem #253: Number Theory | Let $1\leq a_1<a_2<\cdots $ be an infinite sequence of integers such that $a_{i+1}/a_i\to 1$. If every infinite arithmetic progression contains infinitely many integers which are the sum of distinct $a_i$ then every sufficiently large integer is the sum of distinct $a_i$. | Erdős Problems (#253, https://www.erdosproblems.com/253). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.253). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/253",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/253 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,795 | EP-255 | Erdős Problem #255: Discrepancy | Let $z_1,z_2,\ldots \in [0,1]$ be an infinite sequence, and define the discrepancy\[D_N(I) = \#\{ n\leq N: z_n\in I\} - N\lvert I\rvert.\]Must there exist some interval $I\subseteq [0,1]$ such that\[\limsup_{N\to \infty}\lvert D_N(I)\rvert =\infty?\] | Erdős Problems (#255, https://www.erdosproblems.com/255). Maintainer status: PROVED (LEAN). | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/255",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"discrepancy"
] | null | null | null | null | https://www.erdosproblems.com/255 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,796 | EP-259 | Erdős Problem #259: Is the sum\[\sum_{n} \mu(n)^2\frac{n}{2^n}\]irrational? | Is the sum\[\sum_{n} \mu(n)^2\frac{n}{2^n}\]irrational? | Erdős Problems (#259, https://www.erdosproblems.com/259). Maintainer status: PROVED (LEAN). OEIS: A371134. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.259). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/259",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/259 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,797 | EP-262 | Erdős Problem #262: Irrationality | Suppose $a_1<a_2<\cdots$ is a sequence of integers such that for all integer sequences $t_n$ with $t_n\geq 1$ the sum\[\sum_{n=1}^\infty \frac{1}{t_na_n}\]is irrational. How slowly can $a_n$ grow? | Erdős Problems (#262, https://www.erdosproblems.com/262). Maintainer status: SOLVED (LEAN). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/262",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/262 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,798 | EP-266 | Erdős Problem #266: There exists some integer $t\geq 1$ such that\[\sum \frac{1}{a_n+t}\]is irrational | Let $a_n$ be an infinite sequence of positive integers such that $\sum \frac{1}{a_n}$ converges. There exists some integer $t\geq 1$ such that\[\sum \frac{1}{a_n+t}\]is irrational. | Erdős Problems (#266, https://www.erdosproblems.com/266). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.266). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/266",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/266 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,799 | EP-268 | Erdős Problem #268: Number Theory | Let $X\subseteq \mathbb{R}^3$ be the set of all points of the shape\[\left( \sum_{n\in A} \frac{1}{n},\sum_{n\in A}\frac{1}{n+1},\sum_{n\in A} \frac{1}{n+2}\right) \]as $A\subseteq\mathbb{N}$ ranges over all infinite sets with $\sum_{n\in A}\frac{1}{n}<\infty$.
Does $X$ contain an open set? | Erdős Problems (#268, https://www.erdosproblems.com/268). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.268). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/268",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/268 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,800 | EP-270 | Erdős Problem #270: Irrationality | Let $f(n)\to \infty$ as $n\to \infty$. Is it true that\[\sum_{n\geq 1} \frac{1}{(n+1)\cdots (n+f(n))}\]is irrational? | Erdős Problems (#270, https://www.erdosproblems.com/270). Maintainer status: DISPROVED (LEAN). OEIS: A073016. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.270). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/270",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/270 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,801 | EP-275 | Erdős Problem #275: Number Theory, Covering Systems | If a finite system of $r$ congruences $\{ a_i\pmod{n_i}: 1\leq i\leq r\}$ (the $n_i$ are not necessarily distinct) covers $2^r$ consecutive integers then it covers all integers. | Erdős Problems (#275, https://www.erdosproblems.com/275). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.275). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/275",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems"
] | null | null | null | null | https://www.erdosproblems.com/275 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,802 | EP-277 | Erdős Problem #277: Number Theory, Covering Systems | Is it true that, for every $c$, there exists an $n$ such that $\sigma(n)>cn$ but there is no covering system whose moduli all distinct divisors of $n$ (which are $>1$)? | Erdős Problems (#277, https://www.erdosproblems.com/277). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.277). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/277",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems"
] | null | null | null | null | https://www.erdosproblems.com/277 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,803 | EP-280 | Erdős Problem #280: Number Theory, Covering Systems | Let $n_1<n_2<\cdots $ be an infinite sequence of integers with associated $a_k\pmod{n_k}$, such that for some $\epsilon>0$ we have $n_k>(1+\epsilon)k\log k$ for all $k$. Then\[\#\{ m<n_k: m\not\equiv a_i\pmod{n_i} \textrm{ for }1\leq i\leq k\}\neq o(k).\] | Erdős Problems (#280, https://www.erdosproblems.com/280). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.280). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/280",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems"
] | null | null | null | null | https://www.erdosproblems.com/280 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,804 | EP-284 | Erdős Problem #284: \]Is it true that\[f(k)=(1+o(1))\frac{k}{e-1}?\] | Let $f(k)$ be the maximal value of $n_1$ such that there exist $n_1<n_2<\cdots <n_k$ with\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}.\]Is it true that\[f(k)=(1+o(1))\frac{k}{e-1}?\] | Erdős Problems (#284, https://www.erdosproblems.com/284). Maintainer status: PROVED. | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/284",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/284 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,805 | EP-285 | Erdős Problem #285: \]Is it true that\[f(k)=(1+o(1))\frac{e}{e-1}k?\] | Let $f(k)$ be the minimal value of $n_k$ such that there exist $n_1<n_2<\cdots <n_k$ with\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}.\]Is it true that\[f(k)=(1+o(1))\frac{e}{e-1}k?\] | Erdős Problems (#285, https://www.erdosproblems.com/285). Maintainer status: PROVED (LEAN). OEIS: A030659. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.285). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/285",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/285 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,806 | EP-286 | Erdős Problem #286: Number Theory, Unit Fractions | Let $k\geq 2$. Is it true that there exists an interval $I$ of width $(e-1+o(1))k$ and integers $n_1<\cdots<n_k\in I$ such that\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}?\] | Erdős Problems (#286, https://www.erdosproblems.com/286). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.286). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/286",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/286 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,807 | EP-287 | Erdős Problem #287: Number Theory, Unit Fractions | Let $k\geq 2$. Is it true that, for any distinct integers $1<n_1<\cdots <n_k$ such that\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}\]we must have $\max(n_{i+1}-n_i)\geq 3$? | Erdős Problems (#287, https://www.erdosproblems.com/287). Maintainer status: FALSIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.287). | 3 | open | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/287",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/287 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,808 | EP-290 | Erdős Problem #290: Number Theory, Unit Fractions | Let $a\geq 1$. Must there exist some $b>a$ such that\[\sum_{a\leq n\leq b}\frac{1}{n}=\frac{r_1}{s_1}\textrm{ and }\sum_{a\leq n\leq b+1}\frac{1}{n}=\frac{r_2}{s_2},\]with $(r_i,s_i)=1$ and $s_2<s_1$? If so, how does this $b(a)$ grow with $a$? | Erdős Problems (#290, https://www.erdosproblems.com/290). Maintainer status: PROVED (LEAN). OEIS: A375081. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.290). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/290",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/290 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,809 | EP-292 | Erdős Problem #292: Explore $A$. In particular, does $A$ have density $1$? | Let $A$ be the set of $n\in \mathbb{N}$ such that there exist $1\leq m_1<\cdots <m_k=n$ with $\sum\tfrac{1}{m_i}=1$. Explore $A$. In particular, does $A$ have density $1$? | Erdős Problems (#292, https://www.erdosproblems.com/292). Maintainer status: PROVED. OEIS: A092671. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.292). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/292",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/292 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,810 | EP-294 | Erdős Problem #294: Number Theory, Unit Fractions | Let $N\geq 1$ and let $t(N)$ be the least integer $t$ such that there is no solution to\[1=\frac{1}{n_1}+\cdots+\frac{1}{n_k}\]with $t=n_1<\cdots <n_k\leq N$. Estimate $t(N)$. | Erdős Problems (#294, https://www.erdosproblems.com/294). Maintainer status: PROVED. | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/294",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/294 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,811 | EP-296 | Erdős Problem #296: Number Theory, Unit Fractions | Let $N\geq 1$ and let $k(N)$ be maximal such that there are $k$ disjoint $A_1,\ldots,A_k\subseteq \{1,\ldots,N\}$ with $\sum_{n\in A_i}\frac{1}{n}=1$ for all $i$. Estimate $k(N)$. Is it true that $k(N)=o(\log N)$? | Erdős Problems (#296, https://www.erdosproblems.com/296). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.296). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/296",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/296 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,812 | EP-297 | Erdős Problem #297: Number Theory, Unit Fractions | Let $N\geq 1$. How many $A\subseteq \{1,\ldots,N\}$ are there such that $\sum_{n\in A}\frac{1}{n}=1$? | Erdős Problems (#297, https://www.erdosproblems.com/297). Maintainer status: SOLVED. OEIS: A092670. | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/297",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/297 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,813 | EP-298 | Erdős Problem #298: Number Theory, Unit Fractions | Does every set $A\subseteq \mathbb{N}$ of positive density contain some finite $S\subset A$ such that $\sum_{n\in S}\frac{1}{n}=1$? | Erdős Problems (#298, https://www.erdosproblems.com/298). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.298). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/298",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/298 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,814 | EP-299 | Erdős Problem #299: Number Theory, Unit Fractions | Is there an infinite sequence $a_1<a_2<\cdots $ such that $a_{i+1}-a_i=O(1)$ and no finite sum of $\frac{1}{a_i}$ is equal to $1$? | Erdős Problems (#299, https://www.erdosproblems.com/299). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.299). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/299",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/299 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,815 | EP-300 | Erdős Problem #300: Number Theory, Unit Fractions | Let $A(N)$ denote the maximal cardinality of $A\subseteq \{1,\ldots,N\}$ such that $\sum_{n\in S}\frac{1}{n}\neq 1$ for all $S\subseteq A$. Estimate $A(N)$. | Erdős Problems (#300, https://www.erdosproblems.com/300). Maintainer status: SOLVED (LEAN). OEIS: A390393. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.300). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/300",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/300 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
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