id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,916 | EP-523 | Erdős Problem #523: where $\epsilon_k\in \{-1,1\}$ independently uniformly at random for $0\leq k\leq n$ | Let $f(z)=\sum_{0\leq k\leq n} \epsilon_k z^k$ be a random polynomial, where $\epsilon_k\in \{-1,1\}$ independently uniformly at random for $0\leq k\leq n$.
Does there exist some constant $C>0$ such that, almost surely,\[\max_{\lvert z\rvert=1}\left\lvert \sum_{k\leq n}\epsilon_k(t)z^k\right\rvert=(C+o(1))\sqrt{n\log ... | Erdős Problems (#523, https://www.erdosproblems.com/523). 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/523",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"probability",
"polynomials"
] | null | null | null | null | https://www.erdosproblems.com/523 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,917 | EP-525 | Erdős Problem #525: Analysis, Probability | Is it true that all except at most $o(2^n)$ many degree $n$ polynomials with $\pm 1$-valued coefficients $f(z)$ have $\lvert f(z)\rvert <1$ for some $\lvert z\rvert=1$?
What is the behaviour of\[m(f)=\min_{\lvert z\rvert=1}\lvert f(z)\rvert?\] | Erdős Problems (#525, https://www.erdosproblems.com/525). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.525). | 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/525",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"probability",
"polynomials"
] | null | null | null | null | https://www.erdosproblems.com/525 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,918 | EP-526 | Erdős Problem #526: Probability, Geometry | Let $a_n\geq 0$ with $a_n\to 0$ and $\sum a_n=\infty$. Find a necessary and sufficient condition on the $a_n$ such that, if we choose (independently and uniformly) random arcs on the unit circle of length $a_n$, then all the circle is covered with probability $1$. | Erdős Problems (#526, https://www.erdosproblems.com/526). Maintainer status: SOLVED. | 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/526",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"probability",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/526 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,919 | EP-527 | Erdős Problem #527: Analysis, Probability | Let $a_n\in \mathbb{R}$ be such that $\sum_n \lvert a_n\rvert^2=\infty$ and $\lvert a_n\rvert=o(1/\sqrt{n})$. Is it true that, for almost all $\epsilon_n=\pm 1$, there exists some $z$ with $\lvert z\rvert=1$ (depending on the choice of signs) such that\[\sum_n \epsilon_n a_n z^n\]converges? | Erdős Problems (#527, https://www.erdosproblems.com/527). 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/527",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"probability"
] | null | null | null | null | https://www.erdosproblems.com/527 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,920 | EP-532 | Erdős Problem #532: Number Theory, Ramsey Theory | If $\mathbb{N}$ is 2-coloured then is there some infinite set $A\subseteq \mathbb{N}$ such that all finite subset sums\[ \sum_{n\in S}n\](as $S$ ranges over all non-empty finite subsets of $A$) are monochromatic? | Erdős Problems (#532, https://www.erdosproblems.com/532). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.532). | 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/532",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/532 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,921 | EP-534 | Erdős Problem #534: Number Theory, Intersecting Family | What is the largest possible subset $A\subseteq\{1,\ldots,N\}$ which contains $N$ such that $\mathrm{gcd}(a,b)>1$ for all $a\neq b\in A$? | Erdős Problems (#534, https://www.erdosproblems.com/534). Maintainer status: SOLVED. OEIS: A387543, A387698. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.534). | 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/534",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"intersecting-family"
] | null | null | null | null | https://www.erdosproblems.com/534 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,922 | EP-537 | Erdős Problem #537: Number Theory | Let $\epsilon>0$ and $N$ be sufficiently large. If $A\subseteq \{1,\ldots,N\}$ has $\lvert A\rvert \geq \epsilon N$ then must there exist $a_1,a_2,a_3\in A$ and distinct primes $p_1,p_2,p_3$ such that\[a_1p_1=a_2p_2=a_3p_3?\] | Erdős Problems (#537, https://www.erdosproblems.com/537). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.537). | 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/537",
"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/537 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,923 | EP-540 | Erdős Problem #540: Number Theory | Is it true that if $A\subseteq \mathbb{Z}/N\mathbb{Z}$ has size $\gg N^{1/2}$ then there exists some non-empty $S\subseteq A$ such that $\sum_{n\in S}n\equiv 0\pmod{N}$? | Erdős Problems (#540, https://www.erdosproblems.com/540). Maintainer status: PROVED (LEAN). OEIS: A034463. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.540). | 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/540",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/540 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,924 | EP-541 | Erdős Problem #541: Number Theory | Let $a_1,\ldots,a_p$ be (not necessarily distinct) residues modulo $p$, such that there exists some $r$ so that if $S\subseteq [p]$ is non-empty and\[\sum_{i\in S}a_i\equiv 0\pmod{p}\]then $\lvert S\rvert=r$. Must there be at most two distinct residues amongst the $a_i$? | Erdős Problems (#541, https://www.erdosproblems.com/541). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.541). | 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/541",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/541 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,925 | EP-542 | Erdős Problem #542: Number Theory | Is it true that if $A\subseteq\{1,\ldots,n\}$ is a set such that $[a,b]>n$ for all $a\neq b$, where $[a,b]$ is the least common multiple, then\[\sum_{a\in A}\frac{1}{a}\leq \frac{31}{30}?\]Is it true that there must be $\gg n$ many $m\leq n$ which do not divide any $a\in A$? | Erdős Problems (#542, https://www.erdosproblems.com/542). Maintainer status: SOLVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.542). | 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/542",
"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/542 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,926 | EP-546 | Erdős Problem #546: Is it true that\[R(G) \leq 2^{O(m^{1/2})}?\] | Let $G$ be a graph with no isolated vertices and $m$ edges. Is it true that\[R(G) \leq 2^{O(m^{1/2})}?\] | Erdős Problems (#546, https://www.erdosproblems.com/546). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.546). | 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/546",
"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/546 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,927 | EP-547 | Erdős Problem #547: If $T$ is a tree on $n$ vertices then\[R(T) \leq 2n-2.\] | If $T$ is a tree on $n$ vertices then\[R(T) \leq 2n-2.\] | Erdős Problems (#547, https://www.erdosproblems.com/547). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.547). | 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/547",
"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/547 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,928 | EP-548 | Erdős Problem #548: Graph Theory | Let $n\geq k+1$. Every graph on $n$ vertices with at least $\frac{k-1}{2}n+1$ edges contains every tree on $k+1$ vertices. | Erdős Problems (#548, https://www.erdosproblems.com/548). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.548). | 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/548",
"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/548 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,929 | EP-549 | Erdős Problem #549: Graph Theory, Ramsey Theory | If $T$ is a tree which is a bipartite graph with $k$ vertices and $2k$ vertices in the other class then\[R(T)=4k-1.\] | Erdős Problems (#549, https://www.erdosproblems.com/549). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.549). | 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/549",
"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/549 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,930 | EP-551 | Erdős Problem #551: Prove that\[R(C_k,K_n)=(k-1)(n-1)+1\]for $k\geq n\geq 3$ (except when $n=k=3$) | Prove that\[R(C_k,K_n)=(k-1)(n-1)+1\]for $k\geq n\geq 3$ (except when $n=k=3$). | Erdős Problems (#551, https://www.erdosproblems.com/551). Maintainer status: DECIDABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.551). | 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/551",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "decidable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/551 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,931 | EP-553 | Erdős Problem #553: Graph Theory, Ramsey Theory | Let $R(3,3,n)$ denote the smallest integer $m$ such that if we $3$-colour the edges of $K_m$ then there is either a monochromatic triangle in one of the first two colours or a monochromatic $K_n$ in the third colour. Define $R(3,n)$ similarly but with two colours. Show that\[\frac{R(3,3,n)}{R(3,n)}\to \infty\]as $n\to ... | Erdős Problems (#553, https://www.erdosproblems.com/553). Maintainer status: PROVED. OEIS: A000791. | 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/553",
"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/553 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,932 | EP-556 | Erdős Problem #556: Graph Theory, Ramsey Theory | Let $R_3(G)$ denote the minimal $m$ such that if the edges of $K_m$ are $3$-coloured then there must be a monochromatic copy of $G$. Show that\[R_3(C_n) \leq 4n-3.\] | Erdős Problems (#556, https://www.erdosproblems.com/556). Maintainer status: DECIDABLE. OEIS: A389335. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.556). | 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/556",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "decidable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/556 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,933 | EP-559 | Erdős Problem #559: Graph Theory, Ramsey Theory | Let $\hat{R}(G)$ denote the size Ramsey number, the minimal number of edges $m$ such that there is a graph $H$ with $m$ edges that is Ramsey for $G$.
If $G$ has $n$ vertices and maximum degree $d$ then prove that\[\hat{R}(G)\ll_d n.\] | Erdős Problems (#559, https://www.erdosproblems.com/559). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.559). | 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/559",
"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/559 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,934 | EP-565 | Erdős Problem #565: | Let $R^*(G)$ be the induced Ramsey number: the minimal $m$ such that there is a graph $H$ on $m$ vertices such that any $2$-colouring of the edges of $H$ contains an induced monochromatic copy of $G$.
Is it true that\[R^*(G) \leq 2^{O(n)}\]for any graph $G$ on $n$ vertices? | Erdős Problems (#565, https://www.erdosproblems.com/565). 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/565",
"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/565 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,935 | EP-570 | Erdős Problem #570: Graph Theory, Ramsey Theory | Let $k\geq 3$. Is it true that, if $m$ is sufficiently large, for any graph $H$ on $m$ edges without isolated vertices,\[R(C_k,H) \leq 2m+\left\lfloor\frac{k-1}{2}\right\rfloor?\] | Erdős Problems (#570, https://www.erdosproblems.com/570). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.570). | 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/570",
"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/570 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,936 | EP-577 | Erdős Problem #577: Graph Theory | If $G$ is a graph with $4k$ vertices and minimum degree at least $2k$ then $G$ contains $k$ vertex-disjoint $4$-cycles. | Erdős Problems (#577, https://www.erdosproblems.com/577). 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/577",
"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/577 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,937 | EP-578 | Erdős Problem #578: Graph Theory | If $G$ is a random graph on $2^d$ vertices, including each edge with probability $1/2$, then $G$ almost surely contains a copy of $Q_d$ (the $d$-dimensional hypercube with $2^d$ vertices and $d2^{d-1}$ many edges). | Erdős Problems (#578, https://www.erdosproblems.com/578). 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/578",
"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/578 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,938 | EP-580 | Erdős Problem #580: Must $G$ contain every tree on at most $n/2$ vertices? | Let $G$ be a graph on $n$ vertices such that at least $n/2$ vertices have degree at least $n/2$. Must $G$ contain every tree on at most $n/2$ vertices? | Erdős Problems (#580, https://www.erdosproblems.com/580). Maintainer status: DECIDABLE. | 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/580",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "decidable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/580 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,939 | EP-581 | Erdős Problem #581: Determine $f(m)$ | Let $f(m)$ be the maximal $k$ such that a triangle-free graph on $m$ edges must contain a bipartite graph with $k$ edges. Determine $f(m)$. | Erdős Problems (#581, https://www.erdosproblems.com/581). Maintainer status: SOLVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.581). | 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/581",
"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/581 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,940 | EP-582 | Erdős Problem #582: Graph Theory, Ramsey Theory | Does there exist a graph $G$ which contains no $K_4$, and yet any $2$-colouring of the edges produces a monochromatic $K_3$? | Erdős Problems (#582, https://www.erdosproblems.com/582). Maintainer status: PROVED (LEAN). Erdős prize: $100. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.582). | 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/582",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/582 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,941 | EP-583 | Erdős Problem #583: Graph Theory | Every connected graph on $n$ vertices can be partitioned into at most $\lceil n/2\rceil$ edge-disjoint paths. | Erdős Problems (#583, https://www.erdosproblems.com/583). Maintainer status: FALSIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.583). | 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/583",
"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/583 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,942 | EP-586 | Erdős Problem #586: Is there a covering system such that no two of the moduli divide each other? | Is there a covering system such that no two of the moduli divide each other? | Erdős Problems (#586, https://www.erdosproblems.com/586). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.586). | 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/586",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"covering-systems"
] | null | null | null | null | https://www.erdosproblems.com/586 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,943 | EP-587 | Erdős Problem #587: Number Theory | What is the size of the largest $A\subseteq \{1,\ldots,N\}$ such that, for all $\emptyset\neq S\subseteq A$, $\sum_{n\in S}n$ is not a square? | Erdős Problems (#587, https://www.erdosproblems.com/587). Maintainer status: SOLVED. OEIS: A372040. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.587). | 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/587",
"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/587 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,944 | EP-590 | Erdős Problem #590: Set Theory, Ramsey Theory | Let $\alpha$ be the infinite ordinal $\omega^\omega$. Is it true that in any red/blue colouring of the edges of $K_\alpha$ there is either a red $K_\alpha$ or a blue $K_3$? | Erdős Problems (#590, https://www.erdosproblems.com/590). Maintainer status: PROVED (LEAN). Erdős prize: $250. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.590). | 3 | solved | Paul Erdős | null | 10 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/590",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"set-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/590 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,945 | EP-594 | Erdős Problem #594: Graph Theory, Set Theory | Does every graph $G$ with chromatic number $\geq \aleph_1$ contain all sufficiently large odd cycles? | Erdős Problems (#594, https://www.erdosproblems.com/594). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.594). | 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/594",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"set-theory"
] | null | null | null | null | https://www.erdosproblems.com/594 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,946 | EP-599 | Erdős Problem #599: Graph Theory, Set Theory | Let $G$ be a (possibly infinite) graph and $A,B$ be disjoint independent sets of vertices. Must there exist a family $P$ of disjoint paths between $A$ and $B$ and a set $S$ which contains exactly one vertex from each path in $P$, and such that every path between $A$ and $B$ contains at least one vertex from $S$? | Erdős Problems (#599, https://www.erdosproblems.com/599). Maintainer status: PROVED. Erdős-Menger conjecture Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.599). | 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/599",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | Erdős-Menger conjecture | [
"erdos-problems",
"graph-theory",
"set-theory"
] | null | null | null | null | https://www.erdosproblems.com/599 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,947 | EP-605 | Erdős Problem #605: Geometry, Distances | Is there some function $f(n)\to \infty$ as $n\to\infty$ such that there exist $n$ distinct points on the surface of a two-dimensional sphere with at least $f(n)n$ many pairs of points whose distances are the same? | Erdős Problems (#605, https://www.erdosproblems.com/605). 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/605",
"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/605 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,948 | EP-606 | Erdős Problem #606: Geometry | Given any $n$ distinct points in $\mathbb{R}^2$ let $f(n)$ count the number of distinct lines determined by these points. What are the possible values of $f(n)$? | Erdős Problems (#606, https://www.erdosproblems.com/606). Maintainer status: SOLVED. | 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/606",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/606 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,949 | EP-607 | Erdős Problem #607: Geometry | For a set of $n$ points $P\subset \mathbb{R}^2$ let $\ell_1,\ldots,\ell_m$ be the lines determined by $P$, and let $A=\{\lvert \ell_1\cap P\rvert,\ldots,\lvert \ell_m\cap P\rvert\}$.
Let $F(n)$ count the number of possible sets $A$ that can be constructed this way. Is it true that\[F(n) \leq \exp(O(\sqrt{n}))?\] | Erdős Problems (#607, https://www.erdosproblems.com/607). Maintainer status: PROVED. Erdős prize: $250. | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/607",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/607 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,950 | EP-608 | Erdős Problem #608: Are there at least $\frac{2}{9}n^2$ edges of $G$ which are contained in a $C_5$? | Let $G$ be a graph with $n$ vertices and $>n^2/4$ many edges. Are there at least $\frac{2}{9}n^2$ edges of $G$ which are contained in a $C_5$? | Erdős Problems (#608, https://www.erdosproblems.com/608). Maintainer status: DISPROVED (LEAN). | 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/608",
"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/608 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,951 | EP-613 | Erdős Problem #613: Graph Theory, Ramsey | Let $n\geq 3$ and $G$ be a graph with $\binom{2n+1}{2}-\binom{n}{2}-1$ edges. Must $G$ be the union of a bipartite graph and a graph with maximum degree less than $n$? | Erdős Problems (#613, https://www.erdosproblems.com/613). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.613). | 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/613",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey"
] | null | null | null | null | https://www.erdosproblems.com/613 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,952 | EP-615 | Erdős Problem #615: Graph Theory, Ramsey Theory | Does there exist some constant $c>0$ such that if $G$ is a graph with $n$ vertices and $\geq (1/8-c)n^2$ edges then $G$ must contain either a $K_4$ or an independent set on at least $n/\log n$ vertices? | Erdős Problems (#615, https://www.erdosproblems.com/615). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.615). | 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/615",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/615 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,953 | EP-617 | Erdős Problem #617: Graph Theory | Let $r\geq 3$. If the edges of $K_{r^2+1}$ are $r$-coloured then there exist $r+1$ vertices with at least one colour missing on the edges of the induced $K_{r+1}$. | Erdős Problems (#617, https://www.erdosproblems.com/617). Maintainer status: FALSIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.617). | 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/617",
"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/617 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,954 | EP-618 | Erdős Problem #618: Graph Theory | For a triangle-free graph $G$ let $h_2(G)$ be the smallest number of edges that need to be added to $G$ so that it has diameter $2$ and is still triangle-free. Is it true that if $G$ has maximum degree $o(n^{1/2})$ then $h(G)=o(n^2)$? | Erdős Problems (#618, https://www.erdosproblems.com/618). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.618). | 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/618",
"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/618 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,955 | EP-621 | Erdős Problem #621: Graph Theory | Let $G$ be a graph on $n$ vertices, $\alpha_1(G)$ be the maximum number of edges that contain at most one edge from every triangle, and $\tau_1(G)$ be the minimum number of edges that contain at least one edge from every triangle.
Is it true that\[\alpha_1(G)+\tau_1(G) \leq \frac{n^2}{4}?\] | Erdős Problems (#621, https://www.erdosproblems.com/621). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.621). | 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/621",
"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/621 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,956 | EP-622 | Erdős Problem #622: Must $G$ have $\gg 2^{2n}$ subsets that are spanned by a cycle? | Let $G$ be a regular graph with $2n$ vertices and degree $n+1$. Must $G$ have $\gg 2^{2n}$ subsets that are spanned by a cycle? | Erdős Problems (#622, https://www.erdosproblems.com/622). 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/622",
"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/622 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,957 | EP-628 | Erdős Problem #628: Graph Theory, Chromatic Number | Let $G$ be a graph with chromatic number $k$ containing no $K_k$. If $a,b\geq 2$ and $a+b=k+1$ then must there exist two disjoint subgraphs of $G$ with chromatic numbers $\geq a$ and $\geq b$ respectively? | Erdős Problems (#628, https://www.erdosproblems.com/628). Maintainer status: FALSIFIABLE. Erdős-Lovász Tihany Conjecture Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.628). | 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/628",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | Erdős-Lovász Tihany Conjecture | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/628 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,958 | EP-630 | Erdős Problem #630: 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.
Does... | Erdős Problems (#630, https://www.erdosproblems.com/630). Maintainer status: PROVED (LEAN). | 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/630",
"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/630 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,959 | EP-631 | Erdős Problem #631: 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.
Does... | Erdős Problems (#631, https://www.erdosproblems.com/631). 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/631",
"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/631 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,960 | EP-632 | Erdős Problem #632: Graph Theory, Chromatic Number | A graph is $(a,b)$-choosable if for any assignment of a list of $a$ colours to each of its vertices there is a subset of $b$ colours from each list such that the subsets of adjacent vertices are disjoint.
If $G$ is $(a,b)$-choosable then $G$ is $(am,bm)$-choosable for every integer $m\geq 1$. | Erdős Problems (#632, https://www.erdosproblems.com/632). 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/632",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/632 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,961 | EP-636 | Erdős Problem #636: Graph Theory, Ramsey Theory | Suppose $G$ is a graph on $n$ vertices which contains no complete graph or independent set on $\gg \log n$ many vertices. Must $G$ contain $\gg n^{5/2}$ induced subgraphs which pairwise differ in either the number of vertices or the number of edges? | Erdős Problems (#636, https://www.erdosproblems.com/636). 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/636",
"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/636 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,962 | EP-637 | Erdős Problem #637: Graph Theory, Ramsey Theory | If $G$ is a graph on $n$ vertices which contains no complete graph or independent set on $\gg \log n$ vertices then $G$ contains an induced subgraph on $\gg n$ vertices which contains $\gg n^{1/2}$ distinct degrees. | Erdős Problems (#637, https://www.erdosproblems.com/637). 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/637",
"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/637 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,963 | EP-639 | Erdős Problem #639: Graph Theory, Ramsey Theory | Is it true that if the edges of $K_n$ are 2-coloured then there are at most $n^2/4$ many edges which do not occur in a monochromatic triangle? | Erdős Problems (#639, https://www.erdosproblems.com/639). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.639). | 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/639",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/639 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,964 | EP-641 | Erdős Problem #641: Graph Theory | Is there some function $f$ such that for all $k\geq 1$ if a finite graph $G$ has chromatic number $\geq f(k)$ then $G$ has $k$ edge disjoint cycles on the same set of vertices? | Erdős Problems (#641, https://www.erdosproblems.com/641). 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/641",
"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/641 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,965 | EP-645 | Erdős Problem #645: Number Theory, Additive Combinatorics | If $\mathbb{N}$ is 2-coloured then must there exist a monochromatic three-term arithmetic progression $x,x+d,x+2d$ such that $d>x$? | Erdős Problems (#645, https://www.erdosproblems.com/645). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.645). | 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/645",
"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",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/645 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,966 | EP-646 | Erdős Problem #646: Number Theory, Factorials | Let $p_1,\ldots,p_k$ be distinct primes. Are there infinitely many $n$ such that $n!$ is divisible by an even power of each of the $p_i$? | Erdős Problems (#646, https://www.erdosproblems.com/646). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.646). | 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/646",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"factorials"
] | null | null | null | null | https://www.erdosproblems.com/646 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,967 | EP-647 | Erdős Problem #647: Number Theory | Let $\tau(n)$ count the number of divisors of $n$. Is there some $n>24$ such that\[\max_{m<n}(m+\tau(m))\leq n+2?\] | Erdős Problems (#647, https://www.erdosproblems.com/647). Maintainer status: VERIFIABLE. Erdős prize: £25. OEIS: A062249, A087280. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.647). | 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/647",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "verifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/647 | Erdős Problems (erdosproblems.com) | £25 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,968 | EP-648 | Erdős Problem #648: Number Theory | Let $g(n)$ denote the largest $t$ such that there exist integers $2\leq a_1<a_2<\cdots <a_t <n$ such that\[P(a_1)>P(a_2)>\cdots >P(a_t)\]where $P(m)$ is the greatest prime factor of $m$. Estimate $g(n)$. | Erdős Problems (#648, https://www.erdosproblems.com/648). Maintainer status: SOLVED (LEAN). OEIS: A391750. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.648). | 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/648",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/648 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,969 | EP-649 | Erdős Problem #649: Number Theory | Let $P(m)$ denote the greatest prime factor of $m$. Is it true that, for any two primes $p,q$, there exists some integer $n$ such that $P(n)=p$ and $P(n+1)=q$? | Erdős Problems (#649, https://www.erdosproblems.com/649). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.649). | 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/649",
"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/649 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,970 | EP-651 | Erdős Problem #651: Geometry, Convex | Let $f_k(n)$ denote the smallest integer such that any $f_k(n)$ points in general position in $\mathbb{R}^k$ contain $n$ which determine a convex polyhedron. Is it true that\[f_k(n) > (1+c_k)^n\]for some constant $c_k>0$? | Erdős Problems (#651, https://www.erdosproblems.com/651). Maintainer status: DISPROVED (LEAN). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/651",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"convex"
] | null | null | null | null | https://www.erdosproblems.com/651 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,971 | EP-656 | Erdős Problem #656: Number Theory, Additive Combinatorics | Let $A\subset \mathbb{N}$ be a set with positive upper density. Must there exist an infinite set $B\subseteq A$ and integer $t$ such that\[\{b_1+b_2: b_1\neq b_2\in B\}+t\subseteq A?\] | Erdős Problems (#656, https://www.erdosproblems.com/656). 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/656",
"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/656 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,972 | EP-658 | Erdős Problem #658: Additive Combinatorics | Let $\delta>0$ and $N$ be sufficiently large depending on $\delta$. Is it true that if $A\subseteq \{1,\ldots,N\}^2$ has $\lvert A\rvert \geq \delta N^2$ then $A$ must contain the vertices of a square? | Erdős Problems (#658, https://www.erdosproblems.com/658). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.658). | 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/658",
"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/658 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,973 | EP-659 | Erdős Problem #659: Geometry, Distances | Is there a set of $n$ points in $\mathbb{R}^2$ such that every subset of $4$ points determines at least $3$ distances, yet the total number of distinct distances is\[\ll \frac{n}{\sqrt{\log n}}?\] | Erdős Problems (#659, https://www.erdosproblems.com/659). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.659). | 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/659",
"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/659 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,974 | EP-664 | Erdős Problem #664: Combinatorics | Let $c<1$ be some constant and $A_1,\ldots,A_m\subseteq \{1,\ldots,n\}$ be such that $\lvert A_i\rvert >c\sqrt{n}$ for all $i$ and $\lvert A_i\cap A_j\rvert\leq 1$ for all $i\neq j$.
Must there exist some set $B$ such that $B\cap A_i\neq \emptyset$ and $\lvert B\cap A_i\rvert \ll_c 1$ for all $i$? | Erdős Problems (#664, https://www.erdosproblems.com/664). Maintainer status: DISPROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.664). | 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/664",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/664 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,975 | EP-666 | Erdős Problem #666: Graph Theory | Let $Q_n$ be the $n$-dimensional hypercube graph (so that $Q_n$ has $2^n$ vertices and $n2^{n-1}$ edges). Is it true that, for every $\epsilon>0$, if $n$ is sufficiently large, every subgraph of $Q_n$ with\[\geq \epsilon n2^{n-1}\]many edges contains a $C_6$? | Erdős Problems (#666, https://www.erdosproblems.com/666). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.666). | 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/666",
"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/666 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,976 | EP-672 | Erdős Problem #672: Number Theory | Can the product of an arithmetic progression of positive integers $n,n+d,\ldots,n+(k-1)d$ of length $k\geq 4$ (with $(n,d)=1$) be a perfect power? | Erdős Problems (#672, https://www.erdosproblems.com/672). Maintainer status: VERIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.672). | 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/672",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "verifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/672 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,977 | EP-673 | Erdős Problem #673: Number Theory, Divisors | Let $1=d_1<\cdots <d_{\tau(n)}=n$ be the divisors of $n$ and\[G(n) = \sum_{1\leq i<\tau(n)}\frac{d_i}{d_{i+1}}.\]Is it true that $G(n)\to \infty$ for almost all $n$? Can one prove an asymptotic formula for $\sum_{n\leq X}G(n)$? | Erdős Problems (#673, https://www.erdosproblems.com/673). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.673). | 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/673",
"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/673 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,978 | EP-674 | Erdős Problem #674: Are there any integer solutions to $x^xy^y=z^z$ with $x,y,z>1$? | Are there any integer solutions to $x^xy^y=z^z$ with $x,y,z>1$? | Erdős Problems (#674, https://www.erdosproblems.com/674). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.674). | 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/674",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/674 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,979 | EP-678 | Erdős Problem #678: \ldots,n+k\}$ | Let $M(n,k)=[n+1,\ldots,n+k]$ be the least common multiple of $\{n+1,\ldots,n+k\}$.
Are there infinitely many $m,n$ and $k\geq 3$ with $m\geq n+k$ such that\[M(n,k)>M(m,k+1)?\] | Erdős Problems (#678, https://www.erdosproblems.com/678). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.678). | 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/678",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/678 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,980 | EP-682 | Erdős Problem #682: Number Theory, Primes | Is it true that for almost all $n$ there exists some $m\in (p_n,p_{n+1})$ such that\[p(m) \geq p_{n+1}-p_n,\]where $p(m)$ denotes the least prime factor of $m$? | Erdős Problems (#682, https://www.erdosproblems.com/682). Maintainer status: PROVED. OEIS: A386978. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.682). | 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/682",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/682 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,981 | EP-692 | Erdős Problem #692: Number Theory, Divisors | Let $\delta_1(n,m)$ be the density of the set of integers with exactly one divisor in $(n,m)$. Is $\delta_1(n,m)$ unimodular for $m>n+1$ (i.e. increases until some $m$ then decreases thereafter)? For fixed $n$, where does $\delta_1(n,m)$ achieve its maximum? | Erdős Problems (#692, https://www.erdosproblems.com/692). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.692). | 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/692",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"divisors"
] | null | null | null | null | https://www.erdosproblems.com/692 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,982 | EP-697 | Erdős Problem #697: Number Theory, Divisors | Let $\delta(m,\alpha)$ denote the density of the set of integers which are divisible by some $d\equiv 1\pmod{m}$ with $1<d<\exp(m^\alpha)$. Does there exist some $\beta\in (1,\infty)$ such that\[\lim_{m\to \infty}\delta(m,\alpha)\]is $0$ if $\alpha<\beta$ and $1$ if $\alpha>\beta$? | Erdős Problems (#697, https://www.erdosproblems.com/697). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.697). | 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/697",
"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/697 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,983 | EP-698 | Erdős Problem #698: Number Theory, Binomial Coefficients | Is there some $h(n)\to \infty$ such that for all $2\leq i<j\leq n/2$\[\textrm{gcd}\left( \binom{n}{i},\binom{n}{j}\right) \geq h(n)?\] | Erdős Problems (#698, https://www.erdosproblems.com/698). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.698). | 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/698",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"binomial-coefficients"
] | null | null | null | null | https://www.erdosproblems.com/698 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,984 | EP-699 | Erdős Problem #699: Number Theory, Binomial Coefficients | Is it true that for every $1\leq i<j\leq n/2$ there exists some prime $p\geq i$ such that\[p\mid \textrm{gcd}\left(\binom{n}{i}, \binom{n}{j}\right)?\] | Erdős Problems (#699, https://www.erdosproblems.com/699). Maintainer status: FALSIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.699). | 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/699",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"binomial-coefficients"
] | null | null | null | null | https://www.erdosproblems.com/699 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,985 | EP-702 | Erdős Problem #702: Combinatorics | Let $k\geq 4$. If $\mathcal{F}$ is a family of subsets of $\{1,\ldots,n\}$ with $\lvert A\rvert=k$ for all $A\in \mathcal{F}$ and $\lvert \mathcal{F}\rvert >\binom{n-2}{k-2}$ then there are $A,B\in\mathcal{F}$ such that $\lvert A\cap B\rvert=1$. | Erdős Problems (#702, https://www.erdosproblems.com/702). 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/702",
"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/702 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,986 | EP-703 | Erdős Problem #703: Combinatorics | Let $r\geq 1$ and define $T(n,r)$ to be maximal such that there exists a family $\mathcal{F}$ of subsets of $\{1,\ldots,n\}$ of size $T(n,r)$ such that $\lvert A\cap B\rvert\neq r$ for all $A,B\in \mathcal{F}$.
Estimate $T(n,r)$ for $r\geq 2$. In particular, is it true that for every $\epsilon>0$ there exists $\delta>... | Erdős Problems (#703, https://www.erdosproblems.com/703). Maintainer status: PROVED (LEAN). Erdős prize: $250. OEIS: A390645. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.703). | 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/703",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/703 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,987 | EP-707 | Erdős Problem #707: Additive Combinatorics, Sidon Sets | Let $A\subset \mathbb{N}$ be a finite Sidon set. Is there some set $B$ with $A\subseteq B$ which is perfect difference set modulo $p^2+p+1$ for some prime $p$? | Erdős Problems (#707, https://www.erdosproblems.com/707). Maintainer status: DISPROVED (LEAN). Erdős prize: $1000. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.707). | 4 | solved | Paul Erdős | null | 2 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/707",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/707 | Erdős Problems (erdosproblems.com) | $1000 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,988 | EP-715 | Erdős Problem #715: Graph Theory | Does every regular graph of degree $4$ contain a regular subgraph of degree $3$? Is there any $r$ such that every regular graph of degree $r$ must contain a regular subgraph of degree $3$? | Erdős Problems (#715, https://www.erdosproblems.com/715). 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/715",
"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/715 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,989 | EP-716 | Erdős Problem #716: Is it true that\[\mathrm{ex}_3(n,\mathcal{F})=o(n^2)?\] | Let $\mathcal{F}$ be the family of all $3$-uniform hypergraphs with $6$ vertices and $3$ $3$-edges. Is it true that\[\mathrm{ex}_3(n,\mathcal{F})=o(n^2)?\] | Erdős Problems (#716, https://www.erdosproblems.com/716). Maintainer status: PROVED (LEAN). Ruzsa-Szemerédi problem Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.716). | 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/716",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | Ruzsa-Szemerédi problem | [
"erdos-problems",
"graph-theory",
"hypergraphs"
] | null | null | null | null | https://www.erdosproblems.com/716 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,990 | EP-717 | Erdős Problem #717: Is it true that\[\chi(G) \ll \frac{n^{1/2}}{\log n}\sigma(G)?\] | Let $G$ be a graph on $n$ vertices with chromatic number $\chi(G)$ and let $\sigma(G)$ be the maximal $k$ such that $G$ contains a subdivision of $K_k$. Is it true that\[\chi(G) \ll \frac{n^{1/2}}{\log n}\sigma(G)?\] | Erdős Problems (#717, https://www.erdosproblems.com/717). 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/717",
"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/717 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,991 | EP-718 | Erdős Problem #718: Graph Theory | Is there some constant $C>0$ such that any graph on $n$ vertices with $\geq Cr^2n$ edges contains a subdivision of $K_r$? | Erdős Problems (#718, https://www.erdosproblems.com/718). 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/718",
"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/718 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,992 | EP-720 | Erdős Problem #720: Graph Theory, Ramsey Theory | Let $\hat{R}(G)$ denote the size Ramsey number, the minimal number of edges $m$ such that there is a graph $H$ with $m$ edges such that in any $2$-colouring of the edges of $H$ there is a monochromatic copy of $G$.
Is it true that, if $P_n$ is the path of length $n$, then\[\hat{R}(P_n)/n\to \infty\]and\[\hat{R}(P_n)/n... | Erdős Problems (#720, https://www.erdosproblems.com/720). Maintainer status: PROVED. Erdős prize: $100. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.720). | 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/720",
"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/720 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,993 | EP-721 | Erdős Problem #721: Number Theory, Additive Combinatorics | Let $W(3,k)$ be the van der Waerden number defined as the minimum $n$ such that in any red/blue colouring of $\{1,\ldots,n\}$ there exists either a red $3$-term arithmetic progression or a blue $k$-term arithmetic progression.
Give reasonable bounds for $W(3,k)$. In particular, give any non-trivial lower bounds for $W... | Erdős Problems (#721, https://www.erdosproblems.com/721). Maintainer status: SOLVED. OEIS: A171081. | 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/721",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/721 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,994 | EP-722 | Erdős Problem #722: Combinatorics | Let $k>r$ and $n$ be sufficiently large in terms of $k$ and $r$. Does there always exist a block $r-(n,k,1)$ design (or Steiner system with parameters $(n,k,r)$), provided the trivial necessary divisibility conditions $\binom{k-i}{r-i}\mid \binom{n-i}{r-i}$ are satisfied for every $0\leq i<r$?
That is, can one find a ... | Erdős Problems (#722, https://www.erdosproblems.com/722). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.722). | 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/722",
"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/722 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,995 | EP-723 | Erdős Problem #723: If there is a finite projective plane of order $n$ then must $n$ be a prime power? | If there is a finite projective plane of order $n$ then must $n$ be a prime power?
A finite projective plane of order $n$ is a collection of subsets of $\{1,\ldots,n^2+n+1\}$ of size $n+1$ such that every pair of elements is contained in exactly one set. | Erdős Problems (#723, https://www.erdosproblems.com/723). Maintainer status: FALSIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.723). | 3 | open | 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/723",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/723 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,996 | EP-728 | Erdős Problem #728: Number Theory, Factorials | Let $C>0$ and $\epsilon>0$ be sufficiently small. Are there infinitely many integers $a,b,n$ with $a\geq \epsilon n$ and $b\geq \epsilon n$ such that\[a! b! \mid n!(a+b-n)!\]and $a+b>n+C\log n$? | Erdős Problems (#728, https://www.erdosproblems.com/728). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.728). | 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/728",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"factorials"
] | null | null | null | null | https://www.erdosproblems.com/728 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,997 | EP-729 | Erdős Problem #729: Number Theory, Factorials | Let $C>0$ be a constant. Are there infinitely many integers $a,b,n$ with $a+b> n+C\log n$ such that the denominator of\[\frac{n!}{a!b!}\]contains only primes $\ll_C 1$? | Erdős Problems (#729, https://www.erdosproblems.com/729). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.729). | 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/729",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"factorials"
] | null | null | null | null | https://www.erdosproblems.com/729 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,998 | EP-732 | Erdős Problem #732: Combinatorics | Call a sequence $1< X_1\leq \cdots \leq X_m\leq n$ block-compatible if there is a pairwise balanced block design $A_1,\ldots,A_m\subseteq \{1,\ldots,n\}$ such that $\lvert A_i\rvert=X_i$ for $1\leq i\leq m$. (A pairwise block design means that every pair in $\{1,\ldots,n\}$ is contained in exactly one of the $A_i$.)
A... | Erdős Problems (#732, https://www.erdosproblems.com/732). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.732). | 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/732",
"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/732 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,999 | EP-733 | Erdős Problem #733: Combinatorics, Geometry | Call a sequence $1<X_1\leq\cdots X_m\leq n$ line-compatible if there is a set of $n$ points in $\mathbb{R}^2$ such that there are $m$ lines $\ell_1,\ldots,\ell_m$ containing at least two points, and the number of points on $\ell_i$ is exactly $X_i$.
Prove that there are at most\[\exp(O(n^{1/2}))\]many line-compatible ... | Erdős Problems (#733, https://www.erdosproblems.com/733). 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/733",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"combinatorics",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/733 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,000 | EP-735 | Erdős Problem #735: Geometry | Given any $n$ points in $\mathbb{R}^2$ when can one give positive weights to the points such that the sum of the weights of the points along every line containing at least two points is the same? | Erdős Problems (#735, https://www.erdosproblems.com/735). Maintainer status: SOLVED. | 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/735",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/735 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,001 | EP-736 | Erdős Problem #736: Graph Theory, Chromatic Number | Let $G$ be a graph with chromatic number $\aleph_1$. Is there, for every cardinal number $m$, some graph $G_m$ of chromatic number $m$ such that every finite subgraph of $G_m$ is a subgraph of $G$? | Erdős Problems (#736, https://www.erdosproblems.com/736). Maintainer status: NOT PROVABLE. | 3 | partially_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/736",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "not provable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/736 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,002 | EP-737 | Erdős Problem #737: Graph Theory, Chromatic Number | Let $G$ be a graph with chromatic number $\aleph_1$. Must there exist an edge $e$ such that, for all large $n$, $G$ contains a cycle of length $n$ containing $e$? | Erdős Problems (#737, https://www.erdosproblems.com/737). 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/737",
"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/737 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,003 | EP-739 | Erdős Problem #739: Graph Theory, Chromatic Number | Let $\mathfrak{m}$ be an infinite cardinal and $G$ be a graph with chromatic number $\mathfrak{m}$. Is it true that, for every infinite cardinal $\mathfrak{n}< \mathfrak{m}$, there exists a subgraph of $G$ with chromatic number $\mathfrak{n}$? | Erdős Problems (#739, https://www.erdosproblems.com/739). Maintainer status: NOT PROVABLE. | 3 | partially_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/739",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "not provable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/739 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,004 | EP-742 | Erdős Problem #742: Graph Theory | Let $G$ be a graph on $n$ vertices with diameter $2$, such that deleting any edge increases the diameter of $G$. Is it true that $G$ has at most $n^2/4$ edges? | Erdős Problems (#742, https://www.erdosproblems.com/742). Maintainer status: DECIDABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.742). | 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/742",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "decidable"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/742 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,005 | EP-743 | Erdős Problem #743: Can we always write $K_n$ as the edge disjoint union of the $T_k$? | Let $T_2,\ldots,T_n$ be a collection of trees such that $T_k$ has $k$ vertices. Can we always write $K_n$ as the edge disjoint union of the $T_k$? | Erdős Problems (#743, https://www.erdosproblems.com/743). Maintainer status: FALSIFIABLE. tree packing conjecture Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.743). | 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/743",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | tree packing conjecture | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/743 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,006 | EP-744 | Erdős Problem #744: Graph Theory, Chromatic Number | Let $k$ be a large fixed constant. Let $f_k(n)$ be the minimal $m$ such that there exists a graph $G$ on $n$ vertices with chromatic number $k$, such that every proper subgraph has chromatic number $<k$, and $G$ can be made bipartite by deleting $m$ edges.
Is it true that $f_k(n)\to \infty$ as $n\to \infty$? In partic... | Erdős Problems (#744, https://www.erdosproblems.com/744). 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/744",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/744 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,007 | EP-745 | Erdős Problem #745: Graph Theory | Describe the size of the second largest component of the random graph on $n$ vertices, where each edge is included independently with probability $1/n$. | Erdős Problems (#745, https://www.erdosproblems.com/745). 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/745",
"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/745 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,008 | EP-746 | Erdős Problem #746: Graph Theory | Is it true that, almost surely, a random graph on $n$ vertices with $\geq (\tfrac{1}{2}+\epsilon)n\log n$ edges is Hamiltonian? | Erdős Problems (#746, https://www.erdosproblems.com/746). 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/746",
"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/746 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,009 | EP-747 | Erdős Problem #747: Combinatorics, Hypergraphs | How large should $\ell(n)$ be such that, almost surely, a random $3$-uniform hypergraph on $3n$ vertices with $\ell(n)$ edges must contain $n$ vertex-disjoint edges? | Erdős Problems (#747, https://www.erdosproblems.com/747). Maintainer status: SOLVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.747). | 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/747",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"combinatorics",
"hypergraphs"
] | null | null | null | null | https://www.erdosproblems.com/747 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,010 | EP-748 | Erdős Problem #748: Number Theory | Let $f(n)$ count the number of sum-free $A\subseteq \{1,\ldots,n\}$, i.e. $A$ contains no solutions to $a=b+c$ with $a,b,c\in A$. Is it true that\[f(n)=2^{(1+o(1))\frac{n}{2}}?\] | Erdős Problems (#748, https://www.erdosproblems.com/748). Maintainer status: PROVED. Cameron-Erdős conjecture OEIS: A007865. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.748). | 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/748",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | Cameron-Erdős conjecture | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/748 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,011 | EP-751 | Erdős Problem #751: Graph Theory, Chromatic Number | Let $G$ be a graph with chromatic number $\chi(G)=4$. If $m_1<m_2<\cdots$ are the lengths of the cycles in $G$ then can $\min(m_{i+1}-m_i)$ be arbitrarily large? Can this happen if the girth of $G$ is large? | Erdős Problems (#751, https://www.erdosproblems.com/751). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.751). | 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/751",
"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/751 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,012 | EP-752 | Erdős Problem #752: Graph Theory, Cycles | Let $G$ be a graph with minimum degree $k$ and girth $>2s$ (i.e. $G$ contains no cycles of length $\leq 2s$). Must there be $\gg k^s$ many distinct cycle lengths in $G$? | Erdős Problems (#752, https://www.erdosproblems.com/752). 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/752",
"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/752 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,013 | EP-753 | Erdős Problem #753: 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.
Does... | Erdős Problems (#753, https://www.erdosproblems.com/753). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.753). | 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/753",
"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/753 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,014 | EP-754 | Erdős Problem #754: | Let $f(n)$ be maximal such that there exists a set $A$ of $n$ points in $\mathbb{R}^4$ in which every $x\in A$ has at least $f(n)$ points in $A$ equidistant from $x$.
Is it true that $f(n)\leq \frac{n}{2}+O(1)$? | Erdős Problems (#754, https://www.erdosproblems.com/754). Maintainer status: PROVED (LEAN). | 3 | solved | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/754",
"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/754 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,007,015 | EP-755 | Erdős Problem #755: Geometry | The number of equilateral triangles of size $1$ formed by any set of $n$ points in $\mathbb{R}^6$ is at most $(\frac{1}{27}+o(1))n^3$. | Erdős Problems (#755, https://www.erdosproblems.com/755). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.755). | 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/755",
"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/755 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
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