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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,007,016 | EP-756 | Erdős Problem #756: Geometry, Distances | Let $A\subset \mathbb{R}^2$ be a set of $n$ points. Can there be $\gg n$ many distinct distances each of which occurs for more than $n$ many pairs from $A$? | Erdős Problems (#756, https://www.erdosproblems.com/756). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.756). | 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/756",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/756 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,017 | EP-758 | Erdős Problem #758: Graph Theory, Chromatic Number | The cochromatic number of $G$, denoted by $\zeta(G)$, is the minimum number of colours needed to colour the vertices of $G$ such that each colour class induces either a complete graph or empty graph. Let $z(n)$ be the maximum value of $\zeta(G)$ over all graphs $G$ with $n$ vertices.
Determine $z(n)$ for small values ... | Erdős Problems (#758, https://www.erdosproblems.com/758). Maintainer status: SOLVED. | 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/758",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/758 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,018 | EP-759 | Erdős Problem #759: Graph Theory, Chromatic Number | The cochromatic number of $G$, denoted by $\zeta(G)$, is the minimum number of colours needed to colour the vertices of $G$ such that each colour class induces either a complete graph or empty graph.
Let $z(S_n)$ be the maximum value of $\zeta(G)$ over all graphs $G$ which can be embedded on $S_n$, the orientable surf... | Erdős Problems (#759, https://www.erdosproblems.com/759). Maintainer status: SOLVED. | 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/759",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/759 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,019 | EP-760 | Erdős Problem #760: Graph Theory, Chromatic Number | The cochromatic number of $G$, denoted by $\zeta(G)$, is the minimum number of colours needed to colour the vertices of $G$ such that each colour class induces either a complete graph or independent set.
If $G$ is a graph with chromatic number $\chi(G)=m$ then must $G$ contain a subgraph $H$ with\[\zeta(H) \gg \frac{m... | Erdős Problems (#760, https://www.erdosproblems.com/760). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.760). | 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/760",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/760 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,020 | EP-762 | Erdős Problem #762: Graph Theory, Chromatic Number | The cochromatic number of $G$, denoted by $\zeta(G)$, is the minimum number of colours needed to colour the vertices of $G$ such that each colour class induces either a complete graph or empty graph.
Is it true that if $G$ has no $K_5$ and $\zeta(G)\geq 4$ then $\chi(G) \leq \zeta(G)+2$? | Erdős Problems (#762, https://www.erdosproblems.com/762). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.762). | 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/762",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/762 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,021 | EP-763 | Erdős Problem #763: Number Theory, Additive Combinatorics | Let $A\subseteq \mathbb{N}$. Can there exist some constant $c>0$ such that\[\sum_{n\leq N} 1_A\ast 1_A(n) = cN+O(1)?\] | Erdős Problems (#763, https://www.erdosproblems.com/763). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.763). | 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/763",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/763 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,022 | EP-764 | Erdős Problem #764: Number Theory, Additive Combinatorics | Let $A\subseteq \mathbb{N}$. Can there exist some constant $c>0$ such that\[\sum_{n\leq N} 1_A\ast 1_A\ast 1_A(n) = cN+O(1)?\] | Erdős Problems (#764, https://www.erdosproblems.com/764). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.764). | 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/764",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/764 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,023 | EP-765 | Erdős Problem #765: Give an asymptotic formula for $\mathrm{ex}(n;C_4)$ | Give an asymptotic formula for $\mathrm{ex}(n;C_4)$. | Erdős Problems (#765, https://www.erdosproblems.com/765). Maintainer status: SOLVED (LEAN). OEIS: A006855. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.765). | 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/765",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"turan-number"
] | null | null | null | null | https://www.erdosproblems.com/765 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,024 | EP-767 | Erdős Problem #767: Is it true that\[g_k(n)=(k+1)n-(k+1)^2\]for $n$ sufficiently large? | Let $g_k(n)$ be the maximal number of edges possible on a graph with $n$ vertices which does not contain a cycle with $k$ chords incident to a vertex on the cycle. Is it true that\[g_k(n)=(k+1)n-(k+1)^2\]for $n$ sufficiently large? | Erdős Problems (#767, https://www.erdosproblems.com/767). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.767). | 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/767",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"turan-number"
] | null | null | null | null | https://www.erdosproblems.com/767 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,025 | EP-771 | Erdős Problem #771: Number Theory | Let $f(n)$ be maximal such that, for every $m\geq 1$, there exists some $S\subseteq \{1,\ldots,n\}$ with $\lvert S\rvert=f(n)$ such that $m\neq \sum_{a\in A}a$ for all $A\subseteq S$.
Is it true that\[f(n) = \left(\frac{1}{2}+o(1)\right)\frac{n}{\log n}?\] | Erdős Problems (#771, https://www.erdosproblems.com/771). 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/771",
"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/771 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,026 | EP-772 | Erdős Problem #772: Number Theory, Sidon Sets | Let $k\geq 1$ and $H_k(n)$ be the maximal $r$ such that if $A\subset\mathbb{N}$ has $\lvert A\rvert=n$ and $\| 1_A\ast 1_A\|_\infty \leq k$ then $A$ contains a Sidon set of size at least $r$.
Is it true that $H_k(n)/n^{1/2}\to \infty$? Or even $H_k(n) > n^{1/2+c}$ for some constant $c>0$? | Erdős Problems (#772, https://www.erdosproblems.com/772). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.772). | 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/772",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/772 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,027 | EP-775 | Erdős Problem #775: Graph Theory, Hypergraphs | Is there a $3$-uniform hypergraph on $n$ vertices which contains at least $n-O(1)$ different sizes of cliques (maximal complete subgraphs) | Erdős Problems (#775, https://www.erdosproblems.com/775). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.775). | 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/775",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"hypergraphs"
] | null | null | null | null | https://www.erdosproblems.com/775 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,028 | EP-777 | Erdős Problem #777: Graph Theory, Combinatorics | If $\mathcal{F}$ is a family of subsets of $\{1,\ldots,n\}$ then we write $G_{\mathcal{F}}$ for the graph on $\mathcal{F}$ where $A\sim B$ if $A$ and $B$ are comparable - that is, $A\subseteq B$ or vice versa.
Is it true that, if $\epsilon>0$ and $n$ is sufficiently large, whenever $m\leq (2-\epsilon)2^{n/2}$ the grap... | Erdős Problems (#777, https://www.erdosproblems.com/777). Maintainer status: SOLVED. | 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/777",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/777 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,029 | EP-779 | Erdős Problem #779: Number Theory, Primes | Let $n> 1$ and $p_1<\cdots<p_n$ denote the first $n$ primes. Let $P=\prod_{1\leq i\leq n}p_i$. Does there always exist some prime $p$ with $p_n<p<P$ such that $P+p$ is prime? | Erdős Problems (#779, https://www.erdosproblems.com/779). Maintainer status: FALSIFIABLE. OEIS: A005235. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.779). | 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/779",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/779 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,030 | EP-780 | Erdős Problem #780: Combinatorics, Hypergraphs | Suppose $n\geq kr+(t-1)(k-1)$ and the edges of the complete $r$-uniform hypergraph on $n$ vertices are $t$-coloured. Prove that some colour class must contain $k$ pairwise disjoint edges. | Erdős Problems (#780, https://www.erdosproblems.com/780). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.780). | 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/780",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"combinatorics",
"hypergraphs",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/780 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,031 | EP-781 | Erdős Problem #781: Additive Combinatorics | Let $f(k)$ be the minimal $n$ such that any $2$-colouring of $\{1,\ldots,n\}$ contains a monochromatic $k$-term descending wave: a sequence $x_1<\cdots <x_k$ such that, for $1<j<k$,\[x_j \geq \frac{x_{j+1}+x_{j-1}}{2}.\]Estimate $f(k)$. In particular is it true that $f(k)=k^2-k+1$ for all $k$? | Erdős Problems (#781, https://www.erdosproblems.com/781). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.781). | 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/781",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/781 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,032 | EP-784 | Erdős Problem #784: Number Theory | Let $C>0$. Does there exist a $c>0$ (depending on $C$) such that, for all sufficiently large $x$, if $A\subseteq [1,x]$ has $\sum_{n\in A}\frac{1}{n}\leq C$ then\[\#\{ m\leq x: a\nmid m\textrm{ for all }a\in A\}\gg\frac{x}{(\log x)^c}?\] | Erdős Problems (#784, https://www.erdosproblems.com/784). Maintainer status: SOLVED. | 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/784",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/784 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,033 | EP-785 | Erdős Problem #785: Additive Combinatorics | Let $A,B\subseteq \mathbb{N}$ be infinite sets such that $A+B$ contains all large integers. Let $A(x)=\lvert A\cap [1,x]\rvert$ and similarly for $B(x)$. Is it true that if $A(x)B(x)\sim x$ then\[A(x)B(x)-x\to \infty\]as $x\to \infty$? | Erdős Problems (#785, https://www.erdosproblems.com/785). Maintainer status: PROVED (LEAN). exact additive complements Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.785). | 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/785",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | exact additive complements | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/785 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,034 | EP-794 | Erdős Problem #794: Graph Theory, Hypergraphs | Is it true that every $3$-uniform hypergraph on $3n$ vertices with at least $n^3+1$ edges must contain either a subgraph on $4$ vertices with $3$ edges or a subgraph on $5$ vertices with $7$ edges? | Erdős Problems (#794, https://www.erdosproblems.com/794). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.794). | 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/794",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"hypergraphs",
"turan-number"
] | null | null | null | null | https://www.erdosproblems.com/794 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,035 | EP-795 | Erdős Problem #795: Number Theory | Let $g(n)$ be the maximal size of $A\subseteq \{1,\ldots,n\}$ such that the products $\prod_{n\in S}n$ are distinct for all $S\subseteq A$. Is it true that\[g(n) \leq \pi(n)+\pi(n^{1/2})+o\left(\frac{x^{1/2}}{\log n}\right)?\] | Erdős Problems (#795, https://www.erdosproblems.com/795). 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/795",
"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/795 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,036 | EP-797 | Erdős Problem #797: Graph Theory, Chromatic Number | Let $f(d)$ be the maximal acyclic chromatic number of any graph with maximum degree $d$ - that is, the vertices of any graph with maximum degree $d$ can be coloured with $f(d)$ colours such that there is no edge between vertices of the same colour and no cycle containing only two colours.
Estimate $f(d)$. In particula... | Erdős Problems (#797, https://www.erdosproblems.com/797). 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/797",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/797 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,037 | EP-798 | Erdős Problem #798: Geometry | Let $t(n)$ be the minimum number of points in $\{1,\ldots,n\}^2$ such that the $\binom{t}{2}$ lines determined by these points cover all points in $\{1,\ldots,n\}^2$.
Estimate $t(n)$. In particular, is it true that $t(n)=o(n)$? | Erdős Problems (#798, https://www.erdosproblems.com/798). Maintainer status: PROVED (LEAN). OEIS: A116446. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.798). | 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/798",
"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/798 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,038 | EP-799 | Erdős Problem #799: Graph Theory, Chromatic Number | The list chromatic number $\chi_L(G)$ is defined to be the minimal $k$ such that for any assignment of a list of $k$ colours to each vertex of $G$ (perhaps different lists for different vertices) a colouring of each vertex by a colour on its list can be chosen such that adjacent vertices receive distinct colours.
Is i... | Erdős Problems (#799, https://www.erdosproblems.com/799). 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/799",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/799 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,039 | EP-800 | Erdős Problem #800: Graph Theory, Ramsey Theory | If $G$ is a graph on $n$ vertices which has no two adjacent vertices of degree $\geq 3$ then\[R(G)\ll n,\]where the implied constant is absolute. | Erdős Problems (#800, https://www.erdosproblems.com/800). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.800). | 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/800",
"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/800 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,040 | EP-801 | Erdős Problem #801: Graph Theory, Ramsey Theory | If $G$ is a graph on $n$ vertices containing no independent set on $>n^{1/2}$ vertices then there is a set of $\leq n^{1/2}$ vertices containing $\gg n^{1/2}\log n$ edges. | Erdős Problems (#801, https://www.erdosproblems.com/801). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.801). | 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/801",
"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/801 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,041 | EP-803 | Erdős Problem #803: Graph Theory | We call a graph $H$ $D$-balanced (or $D$-almost-regular) if the maximum degree of $H$ is at most $D$ times the minimum degree of $H$.
Is it true that for every $m\geq 1$, if $n$ is sufficiently large, any graph on $n$ vertices with $\geq n\log n$ edges contains a $O(1)$-balanced subgraph with $m$ vertices and $\gg m\l... | Erdős Problems (#803, https://www.erdosproblems.com/803). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.803). | 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/803",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/803 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,042 | EP-804 | Erdős Problem #804: | Let $f(m,n)$ be maximal such that any graph on $n$ vertices in which every induced subgraph on $m$ vertices has an independent set of size at least $\log n$ must contain an independent set of size at least $f(n)$.
Estimate $f(n)$. In particular, is it true that $f((\log n)^2,n) \geq n^{1/2-o(1)}$? Is it true that $f((... | Erdős Problems (#804, https://www.erdosproblems.com/804). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.804). | 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/804",
"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/804 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,043 | EP-806 | Erdős Problem #806: Additive Combinatorics | Let $A\subseteq \{1,\ldots,n\}$ with $\lvert A\rvert \leq n^{1/2}$. Must there exist some $B\subset\mathbb{Z}$ with $\lvert B\rvert=o(n^{1/2})$ such that $A\subseteq B+B$? | Erdős Problems (#806, https://www.erdosproblems.com/806). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.806). | 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/806",
"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/806 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,044 | EP-807 | Erdős Problem #807: Graph Theory | The bipartition number $\tau(G)$ of a graph $G$ is the smallest number of pairwise edge disjoint complete bipartite graphs whose union is $G$. The independence number $\alpha(G)$ is the size of the largest independent subset of $G$.
Is it true that, if $G$ is a random graph on $n$ vertices with edge probability $1/2$,... | Erdős Problems (#807, https://www.erdosproblems.com/807). 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/807",
"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/807 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,045 | EP-808 | Erdős Problem #808: Additive Combinatorics, Graph Theory | Let $c,\epsilon>0$ and $n$ be sufficiently large. If $A\subset \mathbb{N}$ has $\lvert A\rvert=n$ and $G$ is any graph on $A$ with at least $n^{1+c}$ edges then\[\max(\lvert A+_GA\rvert,\lvert A\cdot_G A\rvert) \geq \lvert A\rvert^{1+c-\epsilon},\]where\[A+_GA = \{ a+b: (a,b)\in G\}\]and similarly for $A\cdot_GA$. | Erdős Problems (#808, https://www.erdosproblems.com/808). Maintainer status: DISPROVED. | 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/808",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/808 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,046 | EP-814 | Erdős Problem #814: Graph Theory | Let $k\geq 2$ and $G$ be a graph with $n\geq k-1$ vertices and\[(k-1)(n-k+2)+\binom{k-2}{2}+1\]edges. Does there exist some $c_k>0$ such that $G$ must contain an induced subgraph on at most $(1-c_k)n$ vertices with minimum degree at least $k$? | Erdős Problems (#814, https://www.erdosproblems.com/814). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.814). | 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/814",
"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/814 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,047 | EP-815 | Erdős Problem #815: Graph Theory | Let $k\geq 3$ and $n$ be sufficiently large. Is it true that if $G$ is a graph with $n$ vertices and $2n-2$ edges such that every proper induced subgraph has minimum degree $\leq 2$ then $G$ must contain a copy of $C_k$? | Erdős Problems (#815, https://www.erdosproblems.com/815). 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/815",
"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/815 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,048 | EP-816 | Erdős Problem #816: Graph Theory | Let $G$ be a graph with $2n+1$ vertices and $n^2+n+1$ edges. Must $G$ contain two vertices of the same degree which are joined by a path of length $3$? | Erdős Problems (#816, https://www.erdosproblems.com/816). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.816). | 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/816",
"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/816 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,049 | EP-818 | Erdős Problem #818: Additive Combinatorics | Let $A$ be a finite set of integers such that $\lvert A+A\rvert \ll \lvert A\rvert$. Is it true that\[\lvert AA\rvert \gg \frac{\lvert A\rvert^2}{(\log \lvert A\rvert)^C}\]for some constant $C>0$? | Erdős Problems (#818, https://www.erdosproblems.com/818). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.818). | 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/818",
"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/818 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,050 | EP-822 | Erdős Problem #822: Does the set of integers of the form $n+\phi(n)$ have positive (lower) density? | Does the set of integers of the form $n+\phi(n)$ have positive (lower) density? | Erdős Problems (#822, https://www.erdosproblems.com/822). Maintainer status: PROVED. OEIS: A121048, A155085. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.822). | 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/822",
"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/822 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,051 | EP-823 | Erdős Problem #823: Number Theory | Let $\alpha\geq 1$. Is there a sequence of integers $n_k,m_k$ such that $n_k/m_k\to \alpha$ and $\sigma(n_k)=\sigma(m_k)$ for all $k\geq 1$, where $\sigma$ is the sum of divisors function? | Erdős Problems (#823, https://www.erdosproblems.com/823). 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/823",
"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/823 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,052 | EP-832 | Erdős Problem #832: Graph Theory, Hypergraphs | Let $r\geq 3$ and $k$ be sufficiently large in terms of $r$. Is it true that every $r$-uniform hypergraph with chromatic number $k$ has at least\[\binom{(r-1)(k-1)+1}{r}\]edges, with equality only for the complete graph on $(r-1)(k-1)+1$ vertices? | Erdős Problems (#832, https://www.erdosproblems.com/832). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.832). | 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/832",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"hypergraphs",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/832 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,053 | EP-833 | Erdős Problem #833: Graph Theory, Hypergraphs | Does there exist an absolute constant $c>0$ such that, for all $r\geq 2$, in any $r$-uniform hypergraph with chromatic number $3$ there is a vertex contained in at least $(1+c)^r$ many edges? | Erdős Problems (#833, https://www.erdosproblems.com/833). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.833). | 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/833",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"hypergraphs",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/833 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,054 | EP-834 | Erdős Problem #834: Graph Theory, Hypergraphs | Does there exist a $3$-critical $3$-uniform hypergraph in which every vertex has degree $\geq 7$? | Erdős Problems (#834, https://www.erdosproblems.com/834). Maintainer status: SOLVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.834). | 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/834",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"hypergraphs"
] | null | null | null | null | https://www.erdosproblems.com/834 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,055 | EP-835 | Erdős Problem #835: Graph Theory, Hypergraphs | Does there exist a $k>2$ such that the $k$-sized subsets of $\{1,\ldots,2k\}$ can be coloured with $k+1$ colours such that for every $A\subset \{1,\ldots,2k\}$ with $\lvert A\rvert=k+1$ all $k+1$ colours appear among the $k$-sized subsets of $A$? | Erdős Problems (#835, https://www.erdosproblems.com/835). Maintainer status: VERIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.835). | 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/835",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "verifiable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"hypergraphs"
] | null | null | null | null | https://www.erdosproblems.com/835 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,056 | EP-841 | Erdős Problem #841: Number Theory | Let $t_n$ be minimal such that $\{n+1,\ldots,n+t_n\}$ contains a subset whose product with $n$ is a square number (and let $t_n=0$ if $n$ is itself square). Estimate $t_n$. | Erdős Problems (#841, https://www.erdosproblems.com/841). Maintainer status: SOLVED. OEIS: A092487. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.841). | 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/841",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/841 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,057 | EP-842 | Erdős Problem #842: Does $G$ have chromatic number at most $3$? | Let $G$ be a graph on $3n$ vertices formed by taking $n$ vertex disjoint triangles and adding a Hamiltonian cycle (with all new edges) between these vertices. Does $G$ have chromatic number at most $3$? | Erdős Problems (#842, https://www.erdosproblems.com/842). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.842). | 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/842",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/842 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,058 | EP-843 | Erdős Problem #843: Are the squares Ramsey $2$-complete? | Are the squares Ramsey $2$-complete?
That is, is it true that, in any 2-colouring of the square numbers, every sufficiently large $n\in \mathbb{N}$ can be written as a monochromatic sum of distinct squares? | Erdős Problems (#843, https://www.erdosproblems.com/843). 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/843",
"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/843 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,059 | EP-844 | Erdős Problem #844: for all $a,b\in A$, the product $ab$ is not squarefree | Let $A\subseteq \{1,\ldots,N\}$ be such that, for all $a,b\in A$, the product $ab$ is not squarefree.
Is the maximum size of such an $A$ achieved by taking $A$ to be the set of even numbers and odd non-squarefree numbers? | Erdős Problems (#844, https://www.erdosproblems.com/844). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.844). | 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/844",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"intersecting-family"
] | null | null | null | null | https://www.erdosproblems.com/844 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,060 | EP-845 | Erdős Problem #845: Number Theory | Let $C>0$. Is it true that the set of integers of the form\[n=b_1+\cdots+b_t\textrm{ with }b_1<\cdots<b_t\]where $b_i=2^{k_i}3^{l_i}$ for $1\leq i\leq t$ and $b_t\leq Cb_1$ has density $0$? | Erdős Problems (#845, https://www.erdosproblems.com/845). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.845). | 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/845",
"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/845 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,061 | EP-848 | Erdős Problem #848: Number Theory | Is the maximum size of a set $A\subseteq \{1,\ldots,N\}$ such that $ab+1$ is never squarefree (for all $a,b\in A$) achieved by taking those $n\equiv 7\pmod{25}$? | Erdős Problems (#848, https://www.erdosproblems.com/848). Maintainer status: DECIDABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.848). | 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/848",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "decidable"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/848 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,062 | EP-855 | Erdős Problem #855: Number Theory, Primes | If $\pi(x)$ counts the number of primes in $[1,x]$ then is it true that (for large $x$ and $y$)\[\pi(x+y) \leq \pi(x)+\pi(y)?\] | Erdős Problems (#855, https://www.erdosproblems.com/855). Maintainer status: OPEN. second Hardy-Littlewood conjecture OEIS: A023193. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.855). | 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/855",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | second Hardy-Littlewood conjecture | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/855 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,063 | EP-861 | Erdős Problem #861: Number Theory, Sidon Sets | Let $f(N)$ be the size of the largest Sidon subset of $\{1,\ldots,N\}$ and $A(N)$ be the number of Sidon subsets of $\{1,\ldots,N\}$. Is it true that\[A(N)/2^{f(N)}\to \infty?\]Is it true that\[A(N) = 2^{(1+o(1))f(N)}?\] | Erdős Problems (#861, https://www.erdosproblems.com/861). Maintainer status: SOLVED. OEIS: A143824, A227590, A003022, A143823. | 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/861",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/861 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,064 | EP-862 | Erdős Problem #862: Number Theory, Sidon Sets | Let $A_1(N)$ be the number of maximal Sidon subsets of $\{1,\ldots,N\}$. Is it true that\[A_1(N) < 2^{o(N^{1/2})}?\]Is it true that\[A_1(N) > 2^{N^c}\]for some constant $c>0$? | Erdős Problems (#862, https://www.erdosproblems.com/862). Maintainer status: SOLVED (LEAN). OEIS: A382395. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.862). | 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/862",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/862 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,065 | EP-867 | Erdős Problem #867: Additive Combinatorics | Is it true that if $A=\{a_1<\cdots <a_t\}\subseteq \{1,\ldots,N\}$ has no solutions to\[a_i+a_{i+1}+\cdots+a_j\in A\]then\[\lvert A\rvert \leq \frac{N}{2}+O(1)?\] | Erdős Problems (#867, https://www.erdosproblems.com/867). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.867). | 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/867",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/867 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,066 | EP-868 | Erdős Problem #868: Number Theory, Additive Basis | If $A$ is an additive basis of order $2$, and $1_A\ast 1_A(n)\to \infty$ as $n\to \infty$, then must $A$ contain a minimal additive basis of order $2$? (i.e. such that deleting any element creates infinitely many $n\not\in A+A$)
What if $1_A\ast 1_A(n) >\epsilon \log n$ (for all large $n$, for arbitrary fixed $\epsilo... | Erdős Problems (#868, https://www.erdosproblems.com/868). Maintainer status: SOLVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.868). | 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/868",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/868 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,067 | EP-871 | Erdős Problem #871: Number Theory, Additive Basis | Let $A$ be an additive basis of order $2$, and suppose $1_A\ast 1_A(n)\to \infty$ as $n\to \infty$. Can $A$ be partitioned into two disjoint additive bases of order $2$? | Erdős Problems (#871, https://www.erdosproblems.com/871). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.871). | 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/871",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/871 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,068 | EP-874 | Erdős Problem #874: Number Theory, Additive Combinatorics | Let $k(N)$ denote the size of the largest set $A\subseteq \{1,\ldots,N\}$ such that the sets\[S_r = \{ a_1+\cdots +a_r: a_1<\cdots<a_r\in A\}\]are disjoint for distinct $r\geq 1$. Estimate $k(N)$ - in particular, is it true that $k(N)\sim 2N^{1/2}$? | Erdős Problems (#874, https://www.erdosproblems.com/874). 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/874",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/874 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,069 | EP-877 | Erdős Problem #877: Additive Combinatorics | Let $f_m(n)$ count the number of maximal sum-free subsets $A\subseteq\{1,\ldots,n\}$ - that is, there are no solutions to $a=b+c$ in $A$ and $A$ is maximal with this property. Estimate $f(n)$ - is it true that $f_m(n)=o(2^{n/2})$? | Erdős Problems (#877, https://www.erdosproblems.com/877). Maintainer status: PROVED. OEIS: A121269. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.877). | 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/877",
"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/877 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,070 | EP-880 | Erdős Problem #880: Number Theory, Additive Basis | Let $A\subset\mathbb{N}$ be an additive basis of order $k$. Let $B=\{b_1<b_2<\cdots\}$ be the set of integers which are the sum of $k$ or fewer distinct $a\in A$. Is it true that $b_{n+1}-b_n=O(1)$? (Where the implied constant may depend on both $A$ and $k$.) | Erdős Problems (#880, https://www.erdosproblems.com/880). 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/880",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/880 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,071 | EP-882 | Erdős Problem #882: Number Theory, Primitive Sets | What is the size of the largest $A\subseteq \{1,\ldots,n\}$ such that in the set\[\left\{ \sum_{a\in S} a: \emptyset\neq S\subseteq A\right\}\]no two distinct elements divide each other? | Erdős Problems (#882, https://www.erdosproblems.com/882). Maintainer status: SOLVED. | 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/882",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primitive-sets"
] | null | null | null | null | https://www.erdosproblems.com/882 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,072 | EP-894 | Erdős Problem #894: | Let $A=\{n_1<n_2<\cdots\}\subset \mathbb{N}$ be a lacunary sequence (so there exists some $\epsilon>0$ with $n_{k+1}\geq (1+\epsilon)n_k$ for all $k$).
Is it true that there must exist a finite colouring of $\mathbb{N}$ with no monochromatic solutions to $a-b\in A$? | Erdős Problems (#894, https://www.erdosproblems.com/894). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.894). | 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/894",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/894 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,073 | EP-895 | Erdős Problem #895: Additive Combinatorics, Graph Theory | Is it true that, for all sufficiently large $n$, if $G$ is a triangle-free graph on $\{1,\ldots,n\}$ then there must exist three independent points $a,b,a+b$? | Erdős Problems (#895, https://www.erdosproblems.com/895). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.895). | 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/895",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/895 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,074 | EP-897 | Erdős Problem #897: Number Theory | Let $f(n)$ be an additive function (so that $f(ab)=f(a)+f(b)$ if $(a,b)=1$) such that\[\limsup_{p,k}\frac{f(p^k)}{\log p^k}=\infty.\]Is it true that\[\limsup_n \frac{f(n+1)-f(n)}{\log n}=\infty?\]Or perhaps even\[\limsup_n \frac{f(n+1)}{f(n)}=\infty?\] | Erdős Problems (#897, https://www.erdosproblems.com/897). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.897). | 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/897",
"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/897 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,075 | EP-898 | Erdős Problem #898: Geometry | If $A,B,C\in \mathbb{R}^2$ form a triangle and $P$ is a point in the interior then, if $N$ is where the perpendicular from $P$ to $AB$ meets the triangle, and similarly for $M$ and $L$,\[\overline{PA}+\overline{PB}+\overline{PC}\geq 2(\overline{PM}+\overline{PN}+\overline{PL}).\] | Erdős Problems (#898, https://www.erdosproblems.com/898). Maintainer status: PROVED (LEAN). Erdős-Mordell inequality Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.898). | 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/898",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | Erdős-Mordell inequality | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/898 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,076 | EP-899 | Erdős Problem #899: 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\[\limsup_{N\to \infty}\frac{\lvert (A-A)\cap \{1,\ldots,N\}\rvert}{\lvert A\cap \{1,\ldots,N\}\rvert}=\infty?\] | Erdős Problems (#899, https://www.erdosproblems.com/899). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.899). | 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/899",
"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/899 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,077 | EP-900 | Erdős Problem #900: Graph Theory | There is a function $f:(1/2,\infty)\to \mathbb{R}$ such that $f(c)\to 0$ as $c\to 1/2$ and $f(c)\to 1$ as $c\to \infty$ and every random graph with $n$ vertices and $cn$ edges has (with high probability) a path of length at least $f(c)n$. | Erdős Problems (#900, https://www.erdosproblems.com/900). 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/900",
"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/900 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,078 | EP-903 | Erdős Problem #903: Combinatorics | Let $n=p^2+p+1$ for some prime power $p$, and let $A_1,\ldots,A_t\subseteq \{1,\ldots,n\}$ be a block design (so that every pair $x,y\in \{1,\ldots,n\}$ is contained in exactly one $A_i$).
Is it true that if $t>n$ then $t\geq n+p$? | Erdős Problems (#903, https://www.erdosproblems.com/903). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.903). | 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/903",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/903 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,079 | EP-904 | Erdős Problem #904: Graph Theory | Let $r\geq 2$ and let $t_r(n)$ be the Turán number (the maximal number of edges in a graph on $n$ vertices with no $K_{r+1}$).
If $G$ is a graph with $n$ vertices and $m\geq t_r(n)$ edges there exists a clique on $r$ vertices, say $x_1,\ldots,x_r$, such that\[d(x_1)+\cdots+d(x_r)\geq \frac{2rm}{n}.\] | Erdős Problems (#904, https://www.erdosproblems.com/904). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.904). | 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/904",
"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/904 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,080 | EP-905 | Erdős Problem #905: Graph Theory | Every graph with $n$ vertices and $>n^2/4$ edges contains an edge which is in at least $n/6$ triangles. | Erdős Problems (#905, https://www.erdosproblems.com/905). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.905). | 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/905",
"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/905 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,081 | EP-907 | Erdős Problem #907: Analysis | Let $f:\mathbb{R}\to \mathbb{R}$ be such that $f(x+h)-f(x)$ is continuous for every $h>0$. Is it true that\[f=g+h\]for some continuous $g$ and additive $h$ (i.e. $h(x+y)=h(x)+h(y)$)? | Erdős Problems (#907, https://www.erdosproblems.com/907). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.907). | 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/907",
"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/907 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,082 | EP-908 | Erdős Problem #908: Analysis | Let $f:\mathbb{R}\to \mathbb{R}$ be such that $f(x+h)-f(x)$ is measurable for every $h>0$. Is it true that\[f=g+h+r\]where $g$ is continuous, $h$ is additive (so $h(x+y)=h(x)+h(y)$), and $r(x+h)-r(x)=0$ for every $h$ and almost all (depending on $h$) $x$? | Erdős Problems (#908, https://www.erdosproblems.com/908). Maintainer status: PROVED. | 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/908",
"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/908 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,083 | EP-909 | Erdős Problem #909: Analysis, Topology | Let $n\geq 2$. Is there a space $S$ of dimension $n$ such that $S^2$ also has dimension $n$? | Erdős Problems (#909, https://www.erdosproblems.com/909). Maintainer status: PROVED. | 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/909",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"topology"
] | null | null | null | null | https://www.erdosproblems.com/909 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,084 | EP-910 | Erdős Problem #910: Topology | Does every connected set in $\mathbb{R}^n$ contain a connected subset which is not a point and not homeomorphic to the original set?
If $n\geq 2$ does every connected set in $\mathbb{R}^n$ contain more than $2^{\aleph_0}$ many connected subsets? | Erdős Problems (#910, https://www.erdosproblems.com/910). Maintainer status: DISPROVED. | 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/910",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"topology"
] | null | null | null | null | https://www.erdosproblems.com/910 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,085 | EP-914 | Erdős Problem #914: Graph Theory | Let $r\geq 2$ and $m\geq 1$. Every graph with $rm$ vertices and minimum degree at least $m(r-1)$ contains $m$ vertex disjoint copies of $K_r$. | Erdős Problems (#914, https://www.erdosproblems.com/914). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.914). | 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/914",
"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/914 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,086 | EP-915 | Erdős Problem #915: Must $G$ contain two points which are connected by $m$ disjoint paths? | Let $G$ be a graph with $1+n(m-1)$ vertices and $1+n\binom{m}{2}$ edges. Must $G$ contain two points which are connected by $m$ disjoint paths? | Erdős Problems (#915, https://www.erdosproblems.com/915). Maintainer status: SOLVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.915). | 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/915",
"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/915 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,087 | EP-916 | Erdős Problem #916: Graph Theory, Cycles | Does every graph with $n$ vertices and $2n-2$ edges contain a cycle and another vertex adjacent to three vertices on the cycle? | Erdős Problems (#916, https://www.erdosproblems.com/916). 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/916",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"cycles"
] | null | null | null | null | https://www.erdosproblems.com/916 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,088 | EP-921 | Erdős Problem #921: Graph Theory, Chromatic Number | Let $k\geq 4$ and let $f_k(n)$ be the largest $m$ such that there is a graph on $n$ vertices with chromatic number $k$ in which every odd cycle has length $> m$. Is it true that\[f_k(n) \asymp n^{\frac{1}{k-2}}?\] | Erdős Problems (#921, https://www.erdosproblems.com/921). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.921). | 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/921",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number",
"cycles"
] | null | null | null | null | https://www.erdosproblems.com/921 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,089 | EP-922 | Erdős Problem #922: Graph Theory, Chromatic Number | Let $k\geq 0$. Let $G$ be a graph such that every subgraph $H$ contains an independent set of size $\geq (n-k)/2$, where $n$ is the number of vertices of $H$. Must $G$ have chromatic number at most $k+2$? | Erdős Problems (#922, https://www.erdosproblems.com/922). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.922). | 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/922",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/922 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,090 | EP-923 | Erdős Problem #923: Graph Theory, Chromatic Number | Is it true that, for every $k$, there is some $f(k)$ such that if $G$ has chromatic number $\geq f(k)$ then $G$ contains a triangle-free subgraph with chromatic number $\geq k$? | Erdős Problems (#923, https://www.erdosproblems.com/923). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.923). | 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/923",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/923 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,091 | EP-924 | Erdős Problem #924: Graph Theory, Ramsey Theory | Let $k\geq 2$ and $l\geq 3$. Is there a graph $G$ which contains no $K_{l+1}$ such that every $k$-colouring of the edges of $G$ contains a monochromatic copy of $K_l$? | Erdős Problems (#924, https://www.erdosproblems.com/924). 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/924",
"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/924 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,092 | EP-925 | Erdős Problem #925: Graph Theory, Ramsey Theory | Is there a constant $\delta>0$ such that, for all large $n$, if $G$ is a graph on $n$ vertices which is not Ramsey for $K_3$ (i.e. there exists a 2-colouring of the edges of $G$ with no monochromatic triangle) then $G$ contains an independent set of size $\gg n^{1/3+\delta}$? | Erdős Problems (#925, https://www.erdosproblems.com/925). 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/925",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/925 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,093 | EP-926 | Erdős Problem #926: Graph Theory | Let $k\geq 4$. Is it true that\[\mathrm{ex}(n;H_k) \ll_k n^{3/2},\]where $H_k$ is the graph on vertices $x,y_1,\ldots,y_k,z_1,\ldots,z_{\binom{k}{2}}$, where $x$ is adjacent to all $y_i$ and each pair of $y_i,y_j$ is adjacent to a unique $z_i$. | Erdős Problems (#926, https://www.erdosproblems.com/926). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.926). | 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/926",
"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/926 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,094 | EP-927 | Erdős Problem #927: Graph Theory | Let $g(n)$ be the maximum number of different sizes of cliques that can occur in a graph on $n$ vertices. Estimate $g(n)$ - in particular, is it true that\[g(n)=n-\log_2n-\log_*(n)+O(1),\]where $\log_*(n)$ is the number of iterated logarithms such that $\log\cdots \log n <1$. | Erdős Problems (#927, https://www.erdosproblems.com/927). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.927). | 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/927",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/927 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,095 | EP-937 | Erdős Problem #937: Number Theory, Powerful | Are there infinitely many four-term arithmetic progressions of coprime powerful numbers (i.e. if $p\mid n$ then $p^2\mid n$)? | Erdős Problems (#937, https://www.erdosproblems.com/937). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.937). | 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/937",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"powerful"
] | null | null | null | null | https://www.erdosproblems.com/937 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,096 | EP-941 | Erdős Problem #941: Number Theory, Powerful | Are all large integers the sum of at most three powerful numbers (i.e. if $p\mid n$ then $p^2\mid n$)? | Erdős Problems (#941, https://www.erdosproblems.com/941). Maintainer status: PROVED. OEIS: A056828. | 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/941",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"powerful"
] | null | null | null | null | https://www.erdosproblems.com/941 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,097 | EP-946 | Erdős Problem #946: Number Theory, Divisors | Are there infinitely many $n$ such that $\tau(n)=\tau(n+1)$, where $\tau$ is the divisor function? | Erdős Problems (#946, https://www.erdosproblems.com/946). Maintainer status: PROVED. OEIS: A005237, A284783. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.946). | 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/946",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"divisors"
] | null | null | null | null | https://www.erdosproblems.com/946 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,098 | EP-947 | Erdős Problem #947: Number Theory, Covering Systems | There is no exact covering system - that is, a finite collection of congruence classes $a_i\pmod{n_i}$ with distinct $n_i$ such that every integer satisfies exactly one of these congruence classes. | Erdős Problems (#947, https://www.erdosproblems.com/947). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.947). | 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/947",
"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/947 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,099 | EP-957 | Erdős Problem #957: Geometry, Distances | Let $A\subset \mathbb{R}^2$ be a set of size $n$ and let $\{d_1<\ldots<d_k\}$ be the set of distinct distances determined by $A$. Let $f(d)$ be the number of times the distance $d$ is determined. Is it true that\[f(d_1)f(d_k) \leq (\tfrac{9}{8}+o(1))n^2?\] | Erdős Problems (#957, https://www.erdosproblems.com/957). 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/957",
"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/957 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,100 | EP-958 | Erdős Problem #958: Distances, Geometry | Let $A\subset \mathbb{R}^2$ be a finite set of size $n$, and let $\{d_1,\ldots,d_k\}$ be the set of distances determined by $A$. Let $f(d)$ be the multiplicity of $d$, that is, the number of ordered pairs from $A$ of distance $d$ apart.
Is it true that $k=n-1$ and $\{f(d_i)\}=\{n-1,\ldots,1\}$ if and only if $A$ is a ... | Erdős Problems (#958, https://www.erdosproblems.com/958). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.958). | 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/958",
"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/958 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,101 | EP-964 | Erdős Problem #964: Number Theory, Divisors | Let $\tau(n)$ count the number of divisors of $n$. Is the sequence\[\frac{\tau(n+1)}{\tau(n)}\]everywhere dense in $(0,\infty)$? | Erdős Problems (#964, https://www.erdosproblems.com/964). 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/964",
"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/964 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,102 | EP-965 | Erdős Problem #965: Ramsey Theory | Is it true that, for any $2$-colouring of $\mathbb{R}$, there is a set $A\subseteq \mathbb{R}$ of cardinality $\aleph_1$ such that all sums $a+b$ with $a\neq b$ and $a,b\in A$ are the same colour? | Erdős Problems (#965, https://www.erdosproblems.com/965). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.965). | 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/965",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/965 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,103 | EP-966 | Erdős Problem #966: Number Theory, Additive Combinatorics | Let $k,r\geq 2$. Does there exist a set $A\subseteq \mathbb{N}$ that contains no non-trivial arithmetic progression of length $k+1$, yet in any $r$-colouring of $A$ there must exist a monochromatic non-trivial arithmetic progression of length $k$? | Erdős Problems (#966, https://www.erdosproblems.com/966). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.966). | 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/966",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/966 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,104 | EP-967 | Erdős Problem #967: Number Theory, Analysis | Let $1<a_1<\cdots $ be a sequence of integers such that $\sum\frac{1}{a_i}<\infty$. Is it true that, for every $t\in \mathbb{R}$,\[1+\sum_{k}\frac{1}{a_k^{1+it}}\neq 0?\] | Erdős Problems (#967, https://www.erdosproblems.com/967). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.967). | 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/967",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/967 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,105 | EP-974 | Erdős Problem #974: Analysis | Let $z_1,\ldots,z_n\in \mathbb{C}$ be a sequence such that $z_1=1$. Suppose that the sequence of\[s_k=\sum_{1\leq i\leq n}z_i^k\]contains infinitely many $(n-1)$-tuples of consecutive values of $s_k$ which are all $0$. Then (essentially)\[z_j=e(j/n),\]where $e(x)=e^{2\pi ix}$. | Erdős Problems (#974, https://www.erdosproblems.com/974). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.974). | 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/974",
"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/974 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,106 | EP-977 | Erdős Problem #977: Number Theory | If $P(m)$ is the greatest prime divisor of $m$, then is it true that\[\frac{P(2^n-1)}{n}\to \infty\]as $n\to \infty$? | Erdős Problems (#977, https://www.erdosproblems.com/977). Maintainer status: PROVED. OEIS: A005420, A002583. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.977). | 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/977",
"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/977 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,107 | EP-980 | Erdős Problem #980: Number Theory | Let $k\geq 2$ and $n_k(p)$ denote the least $k$th power nonresidue of $p$. Is it true that\[\sum_{p<x} n_k(p)\sim c_k \frac{x}{\log x}\]for some constant $c_k>0$? | Erdős Problems (#980, https://www.erdosproblems.com/980). Maintainer status: PROVED. OEIS: A053760, A098990. | 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/980",
"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/980 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,108 | EP-981 | Erdős Problem #981: and $f_\epsilon(p)$ be the smallest integer $m$ such that $\sum_{n\leq N} | Let $\epsilon>0$ and $f_\epsilon(p)$ be the smallest integer $m$ such that $\sum_{n\leq N}
\left(\frac{n}{p}\right)<\epsilon N$ for all $N\geq m$. Prove that\[\sum_{p<x}f_\epsilon(p)\sim c_\epsilon \frac{x}{\log x}\]for some $c_\epsilon>0$. | Erdős Problems (#981, https://www.erdosproblems.com/981). 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/981",
"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/981 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,109 | EP-982 | Erdős Problem #982: Geometry, Convex | If $n$ distinct points in $\mathbb{R}^2$ form a convex polygon then some vertex has at least $\lfloor \frac{n}{2}\rfloor$ different distances to other vertices. | Erdős Problems (#982, https://www.erdosproblems.com/982). Maintainer status: FALSIFIABLE. OEIS: A004526. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.982). | 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/982",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"convex",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/982 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,110 | EP-984 | Erdős Problem #984: Arithmetic Progressions, Additive Combinatorics | Can $\mathbb{N}$ be $2$-coloured such that if\[\{a,a+d,\ldots,a+(k-1)d\}\]is a $k$-term monochromatic arithmetic progression then $k\ll_\epsilon a^\epsilon$ for all $\epsilon>0$? | Erdős Problems (#984, https://www.erdosproblems.com/984). 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/984",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"arithmetic-progressions",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/984 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,111 | EP-988 | Erdős Problem #988: Discrepancy | If $P\subseteq S^2$ is a subset of the unit sphere then define the discrepancy\[D(P) = \max_C \lvert \lvert C\cap P\rvert - \alpha_C \lvert P\rvert \rvert,\]where the maximum is taken over all spherical caps $C$, and $\alpha_C$ is the appropriately normalised measure of $C$.
Is it true that\[\min_{\lvert P\rvert=n}D(P... | Erdős Problems (#988, https://www.erdosproblems.com/988). Maintainer status: SOLVED. | 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/988",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"discrepancy"
] | null | null | null | null | https://www.erdosproblems.com/988 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,112 | EP-989 | Erdős Problem #989: Discrepancy | If $A=\{z_1,z_2,\ldots \}\in \mathbb{R}^2$ is an infinite sequence then let\[f(r)=\max_C \left\lvert \lvert A\cap C\rvert-\pi r^2\right\rvert,\]where the maximum is taken over all circles $C$ of radius $r$.
Is $f(r)$ unbounded for every $A$? How fast does $f(r)$ grow? | Erdős Problems (#989, https://www.erdosproblems.com/989). Maintainer status: SOLVED. | 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/989",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"discrepancy"
] | null | null | null | null | https://www.erdosproblems.com/989 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,113 | EP-991 | Erdős Problem #991: Discrepancy | Suppose $A=\{w_1,\ldots,w_n\}\subset S^2$ maximises\[\prod_{i<j}\lvert w_i-w_j\rvert\]over all possible sets of size $n$.
Is it true that\[\max_C\lvert \lvert A\cap C\rvert - \alpha_C n\rvert =o(n),\]where the maximum is taken over all spherical caps $C$ and $\alpha_C$ is the area of $C$ (normalised so that the entire... | Erdős Problems (#991, https://www.erdosproblems.com/991). Maintainer status: PROVED. | 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/991",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"discrepancy"
] | null | null | null | null | https://www.erdosproblems.com/991 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,114 | EP-993 | Erdős Problem #993: The independent set sequence of any tree or forest is unimodal | The independent set sequence of any tree or forest is unimodal.
In other words, if $i_k(G)$ counts the number of independent sets of vertices of size $k$ in a graph $G$, and $T$ is any tree or forest, then for some $m\geq 0$
$$i_{0}(T)\leq i_{1}(T)\leq\cdots\leq i_{m}(T)\geq i_{m+1}(T)\geq i_{m+2}(T)\geq\cdots.$$ | Erdős Problems (#993, https://www.erdosproblems.com/993). Maintainer status: FALSIFIABLE. OEIS: A000055. | 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/993",
"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/993 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,115 | EP-994 | Erdős Problem #994: Analysis, Discrepancy | Let $E\subseteq (0,1)$ be a meaurable subset with Lebesgue measure $\lambda(E)$. Is it true that, for almost all $\alpha$,\[\lim_{n\to \infty}\frac{1}{n}\sum_{1\leq k\leq n}1_{\{k\alpha \}\in E}=\lambda(E)\]for all $E$? | Erdős Problems (#994, https://www.erdosproblems.com/994). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.994). | 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/994",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"discrepancy"
] | null | null | null | null | https://www.erdosproblems.com/994 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.