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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,006,816 | EP-303 | Erdős Problem #303: Number Theory, Unit Fractions | Is it true that in any finite colouring of the integers there exists a monochromatic solution to\[\frac{1}{a}=\frac{1}{b}+\frac{1}{c}\]with distinct $a,b,c$? | Erdős Problems (#303, https://www.erdosproblems.com/303). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.303). | 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/303",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/303 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,817 | EP-305 | Erdős Problem #305: Number Theory, Unit Fractions | For integers $1\leq a<b$ let $D(a,b)$ be the minimal value of $n_k$ such that there exist integers $1\leq n_1<\cdots <n_k$ with\[\frac{a}{b}=\frac{1}{n_1}+\cdots+\frac{1}{n_k}.\]Estimate $D(b)=\max_{1\leq a<b}D(a,b)$. Is it true that\[D(b) \ll b(\log b)^{1+o(1)}?\] | Erdős Problems (#305, https://www.erdosproblems.com/305). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.305). | 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/305",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/305 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,818 | EP-307 | Erdős Problem #307: Number Theory, Unit Fractions | Are there two finite sets of primes $P,Q$ such that\[1=\left(\sum_{p\in P}\frac{1}{p}\right)\left(\sum_{q\in Q}\frac{1}{q}\right)?\] | Erdős Problems (#307, https://www.erdosproblems.com/307). Maintainer status: VERIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.307). | 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/307",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "verifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/307 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,819 | EP-308 | Erdős Problem #308: Number Theory, Unit Fractions | Let $N\geq 1$. What is the smallest integer not representable as the sum of distinct unit fractions with denominators from $\{1,\ldots,N\}$? Is it true that the set of integers representable as such has the shape $\{1,\ldots,m\}$ for some $m$? | Erdős Problems (#308, https://www.erdosproblems.com/308). Maintainer status: PROVED. OEIS: A101877. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.308). | 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/308",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/308 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,820 | EP-309 | Erdős Problem #309: Number Theory, Unit Fractions | Let $N\geq 1$. How many integers can be written as the sum of distinct unit fractions with denominators from $\{1,\ldots,N\}$? Are there $o(\log N)$ such integers? | Erdős Problems (#309, https://www.erdosproblems.com/309). Maintainer status: DISPROVED (LEAN). OEIS: A217693. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.309). | 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/309",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/309 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,821 | EP-310 | Erdős Problem #310: Number Theory, Unit Fractions | Let $\alpha >0$ and $N\geq 1$. Is it true that for any $A\subseteq \{1,\ldots,N\}$ with $\lvert A\rvert \geq \alpha N$ there exists some $S\subseteq A$ such that\[\frac{a}{b}=\sum_{n\in S}\frac{1}{n}\]with $a\leq b =O_\alpha(1)$? | Erdős Problems (#310, https://www.erdosproblems.com/310). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.310). | 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/310",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/310 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,822 | EP-314 | Erdős Problem #314: Number Theory, Unit Fractions | Let $n\geq 1$ and let $m$ be minimal such that $\sum_{n\leq k\leq m}\frac{1}{k}\geq 1$. We define\[\epsilon(n) = \sum_{n\leq k\leq m}\frac{1}{k}-1.\]How small can $\epsilon(n)$ be? Is it true that\[\liminf n^2\epsilon(n)=0?\] | Erdős Problems (#314, https://www.erdosproblems.com/314). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.314). | 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/314",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/314 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,823 | EP-315 | Erdős Problem #315: Number Theory, Unit Fractions | Let $u_1=1$ and $u_{n+1}=u_n(u_n+1)$, so that $\sum_{k\geq 1}\frac{1}{u_k+1}$ and $u_k=\lfloor c_0^{2^k}+1\rfloor$ for $k\geq 1$, where\[c_0=\lim u_n^{1/2^n}=1.264085\cdots.\]Let $a_1<a_2<\cdots $ be any other sequence with $\sum \frac{1}{a_k}=1$. Is it true that\[\liminf a_n^{1/2^n}<c_0=1.264085\cdots?\] | Erdős Problems (#315, https://www.erdosproblems.com/315). Maintainer status: PROVED (LEAN). OEIS: A000058, A076393. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.315). | 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/315",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/315 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,824 | EP-316 | Erdős Problem #316: Number Theory, Unit Fractions | Is it true that if $A\subset \mathbb{N}\backslash\{1\}$ is a finite set with $\sum_{n\in A}\frac{1}{n}<2$ then there is a partition $A=A_1\sqcup A_2$ such that\[\sum_{n\in A_i}\frac{1}{n}<1\]for $i=1,2$? | Erdős Problems (#316, https://www.erdosproblems.com/316). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.316). | 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/316",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/316 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,825 | EP-328 | Erdős Problem #328: Number Theory, Additive Combinatorics | Suppose $A\subseteq\mathbb{N}$ and $C>0$ is such that $1_A\ast 1_A(n)\leq C$ for all $n\in\mathbb{N}$. Can $A$ be partitioned into $t$ many subsets $A_1,\ldots,A_t$ (where $t=t(C)$ depends only on $C$) such that $1_{A_i}\ast 1_{A_i}(n)<C$ for all $1\leq i\leq t$ and $n\in \mathbb{N}$? | Erdős Problems (#328, https://www.erdosproblems.com/328). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.328). | 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/328",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/328 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,826 | EP-331 | Erdős Problem #331: Number Theory, Additive Combinatorics | Let $A,B\subseteq \mathbb{N}$ such that for all large $N$\[\lvert A\cap \{1,\ldots,N\}\rvert \gg N^{1/2}\]and\[\lvert B\cap \{1,\ldots,N\}\rvert \gg N^{1/2}.\]Is it true that there are infinitely many solutions to $a_1-a_2=b_1-b_2\neq 0$ with $a_1,a_2\in A$ and $b_1,b_2\in B$? | Erdős Problems (#331, https://www.erdosproblems.com/331). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.331). | 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/331",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/331 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,827 | EP-333 | Erdős Problem #333: Number Theory, Additive Basis | Let $A\subseteq \mathbb{N}$ be a set of density zero. Does there exist a $B$ such that $A\subseteq B+B$ and\[\lvert B\cap \{1,\ldots,N\}\rvert =o(N^{1/2})\]for all large $N$? | Erdős Problems (#333, https://www.erdosproblems.com/333). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.333). | 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/333",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/333 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,828 | EP-337 | Erdős Problem #337: Number Theory, Additive Combinatorics | Let $A\subseteq \mathbb{N}$ be an additive basis (of any finite order) such that $\lvert A\cap \{1,\ldots,N\}\rvert=o(N)$. Is it true that\[\lim_{N\to \infty}\frac{\lvert (A+A)\cap \{1,\ldots,N\}\rvert}{\lvert A\cap \{1,\ldots,N\}\rvert}=\infty?\] | Erdős Problems (#337, https://www.erdosproblems.com/337). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.337). | 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/337",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/337 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,829 | EP-339 | Erdős Problem #339: Number Theory, Additive Basis | Let $A\subseteq \mathbb{N}$ be a basis of order $r$. Must the set of integers representable as the sum of exactly $r$ distinct elements from $A$ have positive lower density? | Erdős Problems (#339, https://www.erdosproblems.com/339). 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/339",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/339 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,830 | EP-343 | Erdős Problem #343: Number Theory, Complete Sequences | If $A\subseteq \mathbb{N}$ is a multiset of integers such that\[\lvert A\cap \{1,\ldots,N\}\rvert\gg N\]for all $N$ then must $A$ be subcomplete? That is, must\[P(A) = \left\{\sum_{n\in B}n: B\subseteq A\textrm{ finite }\right\}\]contain an infinite arithmetic progression? | Erdős Problems (#343, https://www.erdosproblems.com/343). Maintainer status: PROVED (LEAN). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/343",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"complete-sequences"
] | null | null | null | null | https://www.erdosproblems.com/343 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,831 | EP-344 | Erdős Problem #344: Number Theory, Complete Sequences | If $A\subseteq \mathbb{N}$ is a set of integers such that\[\lvert A\cap \{1,\ldots,N\}\rvert\gg N^{1/2}\]for all $N$ then must $A$ be subcomplete? That is, must\[P(A) = \left\{\sum_{n\in B}n: B\subseteq A\textrm{ finite }\right\}\]contain an infinite arithmetic progression? | Erdős Problems (#344, https://www.erdosproblems.com/344). 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/344",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"complete-sequences"
] | null | null | null | null | https://www.erdosproblems.com/344 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,832 | EP-347 | Erdős Problem #347: Number Theory, Complete Sequences | Is there a sequence $A=\{a_1\leq a_2\leq \cdots\}$ of integers with\[\lim \frac{a_{n+1}}{a_n}=2\]such that\[P(A')= \left\{\sum_{n\in B}n: B\subseteq A'\textrm{ finite }\right\}\]has density $1$ for every cofinite subsequence $A'$ of $A$? | Erdős Problems (#347, https://www.erdosproblems.com/347). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.347). | 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/347",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"complete-sequences"
] | null | null | null | null | https://www.erdosproblems.com/347 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,833 | EP-350 | Erdős Problem #350: Number Theory, Additive Combinatorics | If $A\subset\mathbb{N}$ is a finite set of integers which is dissociated (that is, all of the subset sums are distinct) then\[\sum_{n\in A}\frac{1}{n}<2.\] | Erdős Problems (#350, https://www.erdosproblems.com/350). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.350). | 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/350",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/350 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,834 | EP-353 | Erdős Problem #353: Geometry | Let $A\subseteq \mathbb{R}^2$ be a measurable set with infinite measure. Must $A$ contain the vertices of an isosceles trapezoid of area $1$? What about an isosceles triangle, or a right-angled triangle, or a cyclic quadrilateral, or a convex polygon with congruent sides? | Erdős Problems (#353, https://www.erdosproblems.com/353). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.353). | 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/353",
"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/353 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,835 | EP-355 | Erdős Problem #355: Number Theory, Unit Fractions | Is there a lacunary sequence $A\subseteq \mathbb{N}$ (so that $A=\{a_1<a_2<\cdots\}$ and there exists some $\lambda>1$ such that $a_{n+1}/a_n\geq \lambda$ for all $n\geq 1$) such that\[\left\{ \sum_{a\in A'}\frac{1}{a}: A'\subseteq A\textrm{ finite}\right\}\]contains all rationals in some open interval? | Erdős Problems (#355, https://www.erdosproblems.com/355). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.355). | 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/355",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/355 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,836 | EP-356 | Erdős Problem #356: Number Theory | Is there some $c>0$ such that, for all sufficiently large $n$, there exist integers $a_1<\cdots<a_k\leq n$ such that there are at least $cn^2$ distinct integers of the form $\sum_{u\leq i\leq v}a_i$? | Erdős Problems (#356, https://www.erdosproblems.com/356). Maintainer status: PROVED (LEAN). | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/356",
"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/356 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,837 | EP-360 | Erdős Problem #360: Number Theory | Let $f(n)$ be minimal such that $\{1,\ldots,n-1\}$ can be partitioned into $f(n)$ classes so that $n$ cannot be expressed as a sum of distinct elements from the same class. How fast does $f(n)$ grow? | Erdős Problems (#360, https://www.erdosproblems.com/360). Maintainer status: SOLVED. | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/360",
"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/360 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,838 | EP-362 | Erdős Problem #362: Number Theory | Let $A\subseteq \mathbb{N}$ be a finite set of size $N$. Is it true that, for any fixed $t$, there are\[\ll \frac{2^N}{N^{3/2}}\]many $S\subseteq A$ such that $\sum_{n\in S}n=t$?
If we further ask that $\lvert S\rvert=l$ (for any fixed $l$) then is the number of solutions\[\ll \frac{2^N}{N^2},\]with the implied consta... | Erdős Problems (#362, https://www.erdosproblems.com/362). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.362). | 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/362",
"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/362 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,839 | EP-363 | Erdős Problem #363: Number Theory | Is it true that there are only finitely many collections of disjoint intervals $I_1,\ldots,I_n$ of size $\lvert I_i\rvert \geq 4$ for $1\leq i\leq n$ such that\[\prod_{1\leq i\leq n}\prod_{m\in I_i}m\]is a square? | Erdős Problems (#363, https://www.erdosproblems.com/363). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.363). | 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/363",
"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/363 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,840 | EP-364 | Erdős Problem #364: Number Theory, Powerful | Are there any triples of consecutive positive integers all of which are powerful (i.e. if $p\mid n$ then $p^2\mid n$)? | Erdős Problems (#364, https://www.erdosproblems.com/364). Maintainer status: VERIFIABLE. OEIS: A060355, A076445. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.364). | 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/364",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "verifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"powerful"
] | null | null | null | null | https://www.erdosproblems.com/364 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,841 | EP-366 | Erdős Problem #366: Number Theory, Powerful | Are there any $2$-full $n$ such that $n+1$ is $3$-full? That is, if $p\mid n$ then $p^2\mid n$ and if $p\mid n+1$ then $p^3\mid n+1$. | Erdős Problems (#366, https://www.erdosproblems.com/366). Maintainer status: VERIFIABLE. ambiguous statement OEIS: A060355. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.366). | 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/366",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "verifiable"
} | null | null | null | ambiguous statement | [
"erdos-problems",
"number-theory",
"powerful"
] | null | null | null | null | https://www.erdosproblems.com/366 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,842 | EP-370 | Erdős Problem #370: Number Theory | Are there infinitely many $n$ such that the largest prime factor of $n$ is $<n^{1/2}$ and the largest prime factor of $n+1$ is $<(n+1)^{1/2}$? | Erdős Problems (#370, https://www.erdosproblems.com/370). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.370). | 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/370",
"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/370 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,843 | EP-372 | Erdős Problem #372: Number Theory | Let $P(n)$ denote the largest prime factor of $n$. There are infinitely many $n$ such that $P(n)>P(n+1)>P(n+2)$. | Erdős Problems (#372, https://www.erdosproblems.com/372). Maintainer status: PROVED. OEIS: A071870. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.372). | 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/372",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/372 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,844 | EP-375 | Erdős Problem #375: Number Theory, Primes | Is it true that for any $n,k\geq 1$, if $n+1,\ldots,n+k$ are all composite then there are distinct primes $p_1,\ldots,p_k$ such that $p_i\mid n+i$ for $1\leq i\leq k$? | Erdős Problems (#375, https://www.erdosproblems.com/375). Maintainer status: FALSIFIABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.375). | 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/375",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/375 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,845 | EP-378 | Erdős Problem #378: Number Theory, Binomial Coefficients | Let $r\geq 0$. Does the density of integers $n$ for which $\binom{n}{k}$ is squarefree for at least $r$ values of $1\leq k<n$ exist? Is this density $>0$? | Erdős Problems (#378, https://www.erdosproblems.com/378). 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/378",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"binomial-coefficients"
] | null | null | null | null | https://www.erdosproblems.com/378 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,846 | EP-379 | Erdős Problem #379: Number Theory, Binomial Coefficients | Let $S(n)$ denote the largest integer such that, for all $1\leq k<n$, the binomial coefficient $\binom{n}{k}$ is divisible by $p^{S(n)}$ for some prime $p$ (depending on $k$). Is it true that\[\limsup S(n)=\infty?\] | Erdős Problems (#379, https://www.erdosproblems.com/379). Maintainer status: PROVED (LEAN). OEIS: A048279. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.379). | 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/379",
"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/379 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,847 | EP-381 | Erdős Problem #381: Number Theory, Divisors | A number $n$ is highly composite if $\tau(m)<\tau(n)$ for all $m<n$, where $\tau(m)$ counts the number of divisors of $m$. Let $Q(x)$ count the number of highly composite numbers in $[1,x]$.
Is it true that\[Q(x)\gg_k (\log x)^k\]for every $k\geq 1$? | Erdős Problems (#381, https://www.erdosproblems.com/381). Maintainer status: DISPROVED. OEIS: A002182. | 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/381",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"divisors"
] | null | null | null | null | https://www.erdosproblems.com/381 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,848 | EP-384 | Erdős Problem #384: Number Theory, Binomial Coefficients | If $1<k<n-1$ then $\binom{n}{k}$ is divisible by a prime $p<n/2$ (except $\binom{7}{3}=5\cdot 7$). | Erdős Problems (#384, https://www.erdosproblems.com/384). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.384). | 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/384",
"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/384 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,849 | EP-391 | Erdős Problem #391: Number Theory, Factorials | Let $t(n)$ be maximal such that there is a representation\[n!=a_1\cdots a_n\]with $t(n)=a_1\leq \cdots \leq a_n$. Obtain good bounds for $t(n)/n$. In particular, is it true that\[\lim \frac{t(n)}{n}=\frac{1}{e}?\]Furthermore, does there exist some constant $c>0$ such that\[\frac{t(n)}{n} \leq \frac{1}{e}-\frac{c}{\log ... | Erdős Problems (#391, https://www.erdosproblems.com/391). Maintainer status: PROVED (LEAN). OEIS: A034258, A034259. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.391). | 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/391",
"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/391 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,850 | EP-392 | Erdős Problem #392: Number Theory, Factorials | Let $A(n)$ denote the least value of $t$ such that\[n!=a_1\cdots a_t\]with $a_1\leq \cdots \leq a_t\leq n^2$. Is it true that\[A(n)=\frac{n}{2}-\frac{n}{2\log n}+o\left(\frac{n}{\log n}\right)?\] | Erdős Problems (#392, https://www.erdosproblems.com/392). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.392). | 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/392",
"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/392 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,851 | EP-395 | Erdős Problem #395: Analysis | If $z_1,\ldots,z_n\in \mathbb{C}$ with $\lvert z_i\rvert=1$ then is it true that the probability that\[\lvert \epsilon_1z_1+\cdots+\epsilon_nz_n\rvert \leq \sqrt{2},\]where $\epsilon_i\in \{-1,1\}$ uniformly at random, is $\gg 1/n$? | Erdős Problems (#395, https://www.erdosproblems.com/395). Maintainer status: PROVED (LEAN). reverse Littlewood-Offord problem Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.395). | 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/395",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | reverse Littlewood-Offord problem | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/395 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,852 | EP-397 | Erdős Problem #397: Number Theory, Binomial Coefficients | Are there only finitely many solutions to\[\prod_i \binom{2m_i}{m_i}=\prod_j \binom{2n_j}{n_j}\]with the $m_i,n_j$ distinct? | Erdős Problems (#397, https://www.erdosproblems.com/397). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.397). | 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/397",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"binomial-coefficients"
] | null | null | null | null | https://www.erdosproblems.com/397 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,853 | EP-398 | Erdős Problem #398: Are the only solutions to\[n!=x^2-1\]when $n=4,5,7$? | Are the only solutions to\[n!=x^2-1\]when $n=4,5,7$? | Erdős Problems (#398, https://www.erdosproblems.com/398). Maintainer status: FALSIFIABLE. Brocard-Ramanujan conjecture OEIS: A146968, A141399. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.398). | 3 | open | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | [
"NT-010",
"NT-086"
] | {
"source_url": "https://www.erdosproblems.com/398",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | Brocard-Ramanujan conjecture | [
"erdos-problems",
"number-theory",
"factorials"
] | null | null | null | null | https://www.erdosproblems.com/398 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,854 | EP-399 | Erdős Problem #399: Number Theory, Factorials | Is it true that there are no solutions to\[n! = x^k\pm y^k\]with $x,y,n\in \mathbb{N}$, with $xy>1$ and $k>2$? | Erdős Problems (#399, https://www.erdosproblems.com/399). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.399). | 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/399",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"factorials"
] | null | null | null | null | https://www.erdosproblems.com/399 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,855 | EP-401 | Erdős Problem #401: Number Theory, Factorials | Is there some function $f(r)$ such that $f(r)\to \infty$ as $r\to\infty$, such that, for infinitely many $n$, there exist $a_1,a_2$ with\[a_1+a_2> n+f(r)\log n\]such that $a_1!a_2! \mid n!2^n3^n\cdots p_r^n$? | Erdős Problems (#401, https://www.erdosproblems.com/401). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.401). | 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/401",
"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/401 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,856 | EP-402 | Erdős Problem #402: Number Theory | Prove that, for any finite set $A\subset\mathbb{N}$, there exist $a,b\in A$ such that\[\mathrm{gcd}(a,b)\leq a/\lvert A\rvert.\] | Erdős Problems (#402, https://www.erdosproblems.com/402). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.402). | 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/402",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/402 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,857 | EP-403 | Erdős Problem #403: Number Theory, Factorials | Does the equation\[2^m=a_1!+\cdots+a_k!\]with $a_1<a_2<\cdots <a_k$ have only finitely many solutions? | Erdős Problems (#403, https://www.erdosproblems.com/403). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.403). | 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/403",
"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/403 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,858 | EP-405 | Erdős Problem #405: Is it true that the equation\[(p-1)!+a^{p-1}=p^k\]has only finitely many solutions? | Let $p$ be an odd prime. Is it true that the equation\[(p-1)!+a^{p-1}=p^k\]has only finitely many solutions? | Erdős Problems (#405, https://www.erdosproblems.com/405). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.405). | 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/405",
"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/405 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,859 | EP-407 | Erdős Problem #407: Number Theory | Let $w(n)$ count the number of solutions to\[n=2^a+3^b+2^c3^d\]with $a,b,c,d\geq 0$ integers. Is it true that $w(n)$ is bounded by some absolute constant? | Erdős Problems (#407, https://www.erdosproblems.com/407). Maintainer status: PROVED. OEIS: A387688. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.407). | 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/407",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/407 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,860 | EP-418 | Erdős Problem #418: Are there infinitely many positive integers not of the form $n-\phi(n)$? | Are there infinitely many positive integers not of the form $n-\phi(n)$? | Erdős Problems (#418, https://www.erdosproblems.com/418). Maintainer status: PROVED (LEAN). OEIS: A005278, A263958. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.418). | 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/418",
"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/418 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,861 | EP-419 | Erdős Problem #419: Number Theory, Factorials | If $\tau(n)$ counts the number of divisors of $n$, then what is the set of limit points of\[\frac{\tau((n+1)!)}{\tau(n!)}?\] | Erdős Problems (#419, https://www.erdosproblems.com/419). Maintainer status: SOLVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.419). | 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/419",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"factorials"
] | null | null | null | null | https://www.erdosproblems.com/419 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,862 | EP-426 | Erdős Problem #426: Graph Theory | We say $H$ is a unique subgraph of $G$ if there is exactly one way to find $H$ as a subgraph (not necessarily induced) of $G$. Is there a graph on $n$ vertices with\[\gg \frac{2^{\binom{n}{2}}}{n!}\]many distinct unique subgraphs? | Erdős Problems (#426, https://www.erdosproblems.com/426). Maintainer status: DISPROVED (LEAN). Erdős prize: $25. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.426). | 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/426",
"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/426 | Erdős Problems (erdosproblems.com) | $25 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,863 | EP-427 | Erdős Problem #427: Number Theory, Primes | Is it true that, for every $n$ and $d$, there exists $k$ such that\[d \mid p_{n+1}+\cdots+p_{n+k},\]where $p_r$ denotes the $r$th prime? | Erdős Problems (#427, https://www.erdosproblems.com/427). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.427). | 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/427",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/427 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,864 | EP-429 | Erdős Problem #429: Number Theory | Is it true that, if $A\subseteq \mathbb{N}$ is sparse enough and does not cover all residue classes modulo $p$ for any prime $p$, then there exists some $n$ such that $n+a$ is prime for all $a\in A$? | Erdős Problems (#429, https://www.erdosproblems.com/429). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.429). | 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/429",
"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/429 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,865 | EP-433 | Erdős Problem #433: Number Theory | If $A\subset \mathbb{N}$ is a finite set then let $G(A)$ denote the greatest integer which is not expressible as a finite sum of elements from $A$ (with repetitions allowed). Let\[g(k,n)=\max G(A)\]where the maximum is taken over all $A\subseteq \{1,\ldots,n\}$ of size $\lvert A\rvert=k$ which has no common divisor. Is... | Erdős Problems (#433, https://www.erdosproblems.com/433). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.433). | 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/433",
"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/433 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,866 | EP-434 | Erdős Problem #434: Number Theory | Let $k\leq n$. What choice of $A\subseteq \{1,\ldots,n\}$ (with $\mathrm{gcd}(A)=1$) of size $\lvert A\rvert=k$ maximises the number of integers not representable as the sum of finitely many elements from $A$ (with repetitions allowed)? Is it $\{n,n-1,\ldots,n-k+1\}$? | Erdős Problems (#434, https://www.erdosproblems.com/434). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.434). | 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/434",
"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/434 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,867 | EP-435 | Erdős Problem #435: Number Theory | Let $n\in\mathbb{N}$ with $n\neq p^k$ for any prime $p$ and $k\geq 0$. What is the largest integer not of the form\[\sum_{1\leq i<n}c_i\binom{n}{i}\]where the $c_i\geq 0$ are integers? | Erdős Problems (#435, https://www.erdosproblems.com/435). Maintainer status: PROVED (LEAN). OEIS: A389479. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.435). | 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/435",
"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/435 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,868 | EP-437 | Erdős Problem #437: Number Theory | Let $1\leq a_1<\cdots<a_k\leq x$. How many of the partial products $a_1,a_1a_2,\ldots,a_1\cdots a_k$ can be squares? Is it true that, for any $\epsilon>0$, there can be more than $x^{1-\epsilon}$ squares? | Erdős Problems (#437, https://www.erdosproblems.com/437). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.437). | 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/437",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/437 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,869 | EP-438 | Erdős Problem #438: How large can $A\subseteq \{1,\ldots,N\}$ be if $A+A$ contains no square numbers? | How large can $A\subseteq \{1,\ldots,N\}$ be if $A+A$ contains no square numbers? | Erdős Problems (#438, https://www.erdosproblems.com/438). Maintainer status: SOLVED. OEIS: A363069. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.438). | 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/438",
"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/438 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,870 | EP-439 | Erdős Problem #439: Number Theory, Ramsey Theory | Is it true that, in any finite colouring of the integers, there must be two integers $x\neq y$ of the same colour such that $x+y$ is a square? What about a $k$th power? | Erdős Problems (#439, https://www.erdosproblems.com/439). 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/439",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/439 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,871 | EP-440 | Erdős Problem #440: a_{i+1})\leq x$. Is it true that $A(x) \ll x^{1/2}$? | Let $A=\{a_1<a_2<\cdots\}\subseteq \mathbb{N}$ be infinite and let $A(x)$ count the number of indices for which $\mathrm{lcm}(a_i,a_{i+1})\leq x$. Is it true that $A(x) \ll x^{1/2}$?
How large can\[\liminf \frac{A(x)}{x^{1/2}}\]be? | Erdős Problems (#440, https://www.erdosproblems.com/440). Maintainer status: SOLVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.440). | 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/440",
"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/440 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,872 | EP-441 | Erdős Problem #441: Number Theory | Let $N\geq 1$. What is the size of the largest $A\subset \{1,\ldots,N\}$ such that $[a,b]\leq N$ for all $a,b\in A$, where $[a,b]$ is the least common multiple of $a$ and $b$?
Is it attained by choosing all integers in $[1,(N/2)^{1/2}]$ together with all even integers in $[(N/2)^{1/2},(2N)^{1/2}]$? | Erdős Problems (#441, https://www.erdosproblems.com/441). Maintainer status: DISPROVED (LEAN). OEIS: A068509. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.441). | 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/441",
"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/441 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,873 | EP-442 | Erdős Problem #442: Number Theory | Is it true that if $A\subseteq\mathbb{N}$ is such that\[\frac{1}{\log\log x}\sum_{n\in A\cap [1,x)}\frac{1}{n}\to \infty\]then\[\left(\sum_{n\in A\cap [1,x)}\frac{1}{n}\right)^{-2} \sum_{\substack{a,b\in A\cap (1,x]\\ a<b}}\frac{1}{\mathrm{lcm}(a,b)}\to \infty?\] | Erdős Problems (#442, https://www.erdosproblems.com/442). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.442). | 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/442",
"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/442 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,874 | EP-443 | Erdős Problem #443: Number Theory | Let $m,n\geq 1$. What is\[\# \{ k(m-k): 1\leq k\leq m/2\} \cap \{ l(n-l): 1\leq l\leq n/2\}?\]Can it be arbitrarily large? Is it $\leq (mn)^{o(1)}$ for all sufficiently large $m,n$? | Erdős Problems (#443, https://www.erdosproblems.com/443). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.443). | 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/443",
"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/443 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,875 | EP-444 | Erdős Problem #444: Number Theory, Divisors | Let $A\subseteq\mathbb{N}$ be infinite and $d_A(n)$ count the number of $a\in A$ which divide $n$. Is it true that, for every $k$,\[\limsup_{x\to \infty} \frac{\max_{n<x}d_A(n)}{\left(\sum_{n\in A\cap[1,x)}\frac{1}{n}\right)^k}=\infty?\] | Erdős Problems (#444, https://www.erdosproblems.com/444). 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/444",
"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/444 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,876 | EP-446 | Erdős Problem #446: Number Theory, Divisors | Let $\delta(n)$ denote the density of integers which are divisible by some integer in $(n,2n)$. What is the growth rate of $\delta(n)$?
If $\delta_1(n)$ is the density of integers which have exactly one divisor in $(n,2n)$ then is it true that $\delta_1(n)=o(\delta(n))$? | Erdős Problems (#446, https://www.erdosproblems.com/446). Maintainer status: SOLVED. OEIS: A074738, A399690, A399691, A399697, A399698. | 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/446",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"divisors"
] | null | null | null | null | https://www.erdosproblems.com/446 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,877 | EP-447 | Erdős Problem #447: Combinatorics | How large can a union-free collection $\mathcal{F}$ of subsets of $[n]$ be? By union-free we mean there are no solutions to $A\cup B=C$ with distinct $A,B,C\in \mathcal{F}$. Must $\lvert \mathcal{F}\rvert =o(2^n)$? Perhaps even\[\lvert \mathcal{F}\rvert <(1+o(1))\binom{n}{\lfloor n/2\rfloor}?\] | Erdős Problems (#447, https://www.erdosproblems.com/447). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.447). | 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/447",
"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/447 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,878 | EP-448 | Erdős Problem #448: Number Theory, Divisors | Let $\tau(n)$ count the divisors of $n$ and $\tau^+(n)$ count the number of $k$ such that $n$ has a divisor in $[2^k,2^{k+1})$. Is it true that, for all $\epsilon>0$,\[\tau^+(n) < \epsilon \tau(n)\]for almost all $n$? | Erdős Problems (#448, https://www.erdosproblems.com/448). Maintainer status: DISPROVED (LEAN). OEIS: A397433. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.448). | 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/448",
"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/448 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,879 | EP-449 | Erdős Problem #449: Number Theory, Divisors | Let $r(n)$ count the number of $d_1,d_2$ such that $d_1\mid n$ and $d_2\mid n$ and $d_1<d_2<2d_1$. Is it true that, for every $\epsilon>0$,\[r(n) < \epsilon \tau(n)\]for almost all $n$, where $\tau(n)$ is the number of divisors of $n$? | Erdős Problems (#449, https://www.erdosproblems.com/449). Maintainer status: DISPROVED. OEIS: A399440. | 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/449",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"divisors"
] | null | null | null | null | https://www.erdosproblems.com/449 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,880 | EP-453 | Erdős Problem #453: Number Theory | Is it true that, for all sufficiently large $n$, there exists some $i<n$ such that\[p_n^2 < p_{n+i}p_{n-i},\]where $p_k$ is the $k$th prime? | Erdős Problems (#453, https://www.erdosproblems.com/453). Maintainer status: DISPROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.453). | 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... | [
"GUY-A14a"
] | {
"source_url": "https://www.erdosproblems.com/453",
"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/453 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,881 | EP-458 | Erdős Problem #458: Number Theory, Primes | Let $[1,\ldots,n]$ denote the least common multiple of $\{1,\ldots,n\}$. Is it true that, for all $k\geq 1$,\[[1,\ldots,p_{k+1}-1]< p_k[1,\ldots,p_k]?\] | Erdős Problems (#458, https://www.erdosproblems.com/458). Maintainer status: FALSIFIABLE. OEIS: A056604. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.458). | 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/458",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/458 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,882 | EP-459 | Erdős Problem #459: v)$ is composed entirely of primes dividing $uv$. Estimate $f(u)$ | Let $f(u)$ be the largest $v$ such that no $m\in (u,v)$ is composed entirely of primes dividing $uv$. Estimate $f(u)$. | Erdős Problems (#459, https://www.erdosproblems.com/459). Maintainer status: SOLVED (LEAN). OEIS: A289280. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.459). | 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/459",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/459 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,883 | EP-464 | Erdős Problem #464: Number Theory | Let $A=\{n_1<n_2<\cdots\}\subset \mathbb{N}$ be a lacunary sequence (so there exists some $\epsilon>0$ with $n_{k+1}\geq (1+\epsilon)n_k$ for all $k$). Must there exist an irrational $\theta$ such that\[\{ \|\theta n_k\|: k\geq 1\}\]is not dense in $[0,1]$ (where $\| x\|$ is the distance to the nearest integer)? | Erdős Problems (#464, https://www.erdosproblems.com/464). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.464). | 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/464",
"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/464 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,884 | EP-465 | Erdős Problem #465: Number Theory | Let $N(X,\delta)$ denote the maximum number of points $P_1,\ldots,P_n$ which can be chosen in a circle of radius $X$ such that\[\| \lvert P_i-P_j\rvert \| \geq \delta\]for all $1\leq i<j\leq n$. (Here $\|x\|$ is the distance from $x$ to the nearest integer.)
Is it true that, for any $0<\delta<1/2$, we have\[N(X,\delta... | Erdős Problems (#465, https://www.erdosproblems.com/465). 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/465",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/465 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,885 | EP-466 | Erdős Problem #466: Number Theory | Let $N(X,\delta)$ denote the maximum number of points $P_1,\ldots,P_n$ which can be chosen in a circle of radius $X$ such that\[\| \lvert P_i-P_j\rvert \| \geq \delta\]for all $1\leq i<j\leq n$. (Here $\|x\|$ is the distance from $x$ to the nearest integer.)
Is there some $\delta>0$ such that\[\lim_{x\to \infty}N(X,\d... | Erdős Problems (#466, https://www.erdosproblems.com/466). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.466). | 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/466",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/466 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,886 | EP-471 | Erdős Problem #471: Number Theory | Given a finite set of primes $Q=Q_0$, define a sequence of sets $Q_i$ by letting $Q_{i+1}$ be $Q_i$ together with all primes formed by adding three distinct elements of $Q_i$. Is there some initial choice of $Q$ such that the $Q_i$ become arbitrarily large? | Erdős Problems (#471, https://www.erdosproblems.com/471). 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/471",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/471 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,887 | EP-473 | Erdős Problem #473: Number Theory | Is there a permutation $a_1,a_2,\ldots$ of the positive integers such that $a_k+a_{k+1}$ is always prime? | Erdős Problems (#473, https://www.erdosproblems.com/473). Maintainer status: PROVED. OEIS: A055265. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.473). | 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/473",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/473 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,888 | EP-474 | Erdős Problem #474: Set Theory, Ramsey Theory | Under what set theoretic assumptions is it true that $\mathbb{R}^2$ can be $3$-coloured such that, for every uncountable $A\subseteq \mathbb{R}^2$, $A^2$ contains a pair of each colour? | Erdős Problems (#474, https://www.erdosproblems.com/474). Maintainer status: NOT PROVABLE. Erdős prize: $100. | 3 | partially_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/474",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "not provable"
} | null | null | null | null | [
"erdos-problems",
"set-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/474 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
30,006,889 | EP-475 | Erdős Problem #475: Number Theory, Additive Combinatorics | Let $p$ be a prime. Given any finite set $A\subseteq \mathbb{F}_p\backslash \{0\}$, is there always a rearrangement $A=\{a_1,\ldots,a_t\}$ such that all partial sums $\sum_{1\leq k\leq m}a_{k}$ are distinct, for all $1\leq m\leq t$? | Erdős Problems (#475, https://www.erdosproblems.com/475). Maintainer status: DECIDABLE. | 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/475",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "decidable"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/475 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,890 | EP-476 | Erdős Problem #476: Number Theory, Additive Combinatorics | Let $A\subseteq \mathbb{F}_p$. Let\[A\hat{+}A = \{ a+b: a\neq b \in A\}.\]Is it true that\[\lvert A\hat{+}A\rvert \geq \min(2\lvert A\rvert-3,p)?\] | Erdős Problems (#476, https://www.erdosproblems.com/476). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.476). | 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/476",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/476 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,891 | EP-480 | Erdős Problem #480: Number Theory | Let $x_1,x_2,\ldots\in [0,1]$ be an infinite sequence. Is it true that\[\inf_n \liminf_{m\to \infty} n \lvert x_{m+n}-x_m\rvert\leq 5^{-1/2}\approx 0.447?\] | Erdős Problems (#480, https://www.erdosproblems.com/480). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.480). | 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/480",
"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/480 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,892 | EP-481 | Erdős Problem #481: Number Theory | Let $a_1,\ldots,a_r,b_1,\ldots,b_r\in \mathbb{N}$ such that $\sum_{i}\frac{1}{a_i}>1$. For any finite sequence of $n$ (not necessarily distinct) integers $A=(x_1,\ldots,x_n)$ let $T(A)$ denote the sequence of length $rn$ given by\[(a_ix_j+b_i)_{1\leq j\leq n, 1\leq i\leq r}.\]Prove that, if $A_1=(1)$ and $A_{i+1}=T(A_i... | Erdős Problems (#481, https://www.erdosproblems.com/481). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.481). | 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/481",
"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/481 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,893 | EP-482 | Erdős Problem #482: Number Theory | Define a sequence by $a_1=1$ and\[a_{n+1}=\lfloor\sqrt{2}(a_n+1/2)\rfloor\]for $n\geq 1$. The difference $a_{2n+1}-2a_{2n-1}$ is the $n$th digit in the binary expansion of $\sqrt{2}$.
Find similar results for $\theta=\sqrt{m}$, and other algebraic numbers. | Erdős Problems (#482, https://www.erdosproblems.com/482). Maintainer status: SOLVED. OEIS: A004539. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.482). | 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/482",
"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/482 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,894 | EP-484 | Erdős Problem #484: Number Theory, Additive Combinatorics | Prove that there exists an absolute constant $c>0$ such that, whenever $\{1,\ldots,N\}$ is $k$-coloured (and $N$ is large enough depending on $k$) then there are at least $cN$ many integers in $\{1,\ldots,N\}$ which are representable as a monochromatic sum (that is, $a+b$ where $a,b\in \{1,\ldots,N\}$ are in the same c... | Erdős Problems (#484, https://www.erdosproblems.com/484). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.484). | 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/484",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/484 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,895 | EP-485 | Erdős Problem #485: Analysis, Polynomials | Let $f(k)$ be the minimum number of terms in $P(x)^2$, where $P\in \mathbb{Q}[x]$ ranges over all polynomials with exactly $k$ non-zero terms. Is it true that $f(k)\to\infty$ as $k\to \infty$? | Erdős Problems (#485, https://www.erdosproblems.com/485). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.485). | 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/485",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"polynomials"
] | null | null | null | null | https://www.erdosproblems.com/485 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,896 | EP-487 | Erdős Problem #487: Number Theory | Let $A\subseteq \mathbb{N}$ have positive density. Must there exist distinct $a,b,c\in A$ such that $[a,b]=c$ (where $[a,b]$ is the least common multiple of $a$ and $b$)? | Erdős Problems (#487, https://www.erdosproblems.com/487). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.487). | 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/487",
"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/487 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,897 | EP-490 | Erdős Problem #490: Is it true that\[\lvert A\rvert \lvert B\rvert \ll \frac{N^2}{\log N}?\] | Let $A,B\subseteq \{1,\ldots,N\}$ be such that all the products $ab$ with $a\in A$ and $b\in B$ are distinct. Is it true that\[\lvert A\rvert \lvert B\rvert \ll \frac{N^2}{\log N}?\] | Erdős Problems (#490, https://www.erdosproblems.com/490). Maintainer status: PROVED (LEAN). OEIS: A397205. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.490). | 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/490",
"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/490 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,898 | EP-491 | Erdős Problem #491: Number Theory | Let $f:\mathbb{N}\to \mathbb{R}$ be an additive function (i.e. $f(ab)=f(a)+f(b)$ whenever $(a,b)=1$). If there is a constant $c$ such that $\lvert f(n+1)-f(n)\rvert <c$ for all $n$ then must there exist some $c'$ such that\[f(n)=c'\log n+O(1)?\] | Erdős Problems (#491, https://www.erdosproblems.com/491). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.491). | 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/491",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/491 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,899 | EP-492 | Erdős Problem #492: Number Theory | Let $A=\{a_1<a_2<\cdots\}\subseteq \mathbb{N}$ be infinite such that $a_{i+1}/a_i\to 1$. For any $x\geq a_1$ let\[f(x) = \frac{x-a_i}{a_{i+1}-a_i}\in [0,1),\]where $x\in [a_i,a_{i+1})$. Is it true that, for almost all $\alpha$, the sequence $f(\alpha n)$ is uniformly distributed in $[0,1)$? | Erdős Problems (#492, https://www.erdosproblems.com/492). Maintainer status: DISPROVED. | 3 | solved | Paul Erdős | null | 1 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/492",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/492 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,900 | EP-493 | Erdős Problem #493: Number Theory | Does there exist a $k$ such that every sufficiently large integer can be written in the form\[\prod_{i=1}^k a_i - \sum_{i=1}^k a_i\]for some integers $a_i\geq 2$? | Erdős Problems (#493, https://www.erdosproblems.com/493). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.493). | 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/493",
"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/493 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,901 | EP-494 | Erdős Problem #494: Analysis, Additive Combinatorics | If $A\subset \mathbb{C}$ is a finite set and $k\geq 1$ then let\[A_k = \{ z_1+\cdots+z_k: z_i\in A\textrm{ distinct}\}.\]For $k>2$ does the multiset $A_k$ (together with the size of $A$) uniquely determine the set $A$? | Erdős Problems (#494, https://www.erdosproblems.com/494). Maintainer status: PROVED. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.494). | 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/494",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/494 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,902 | EP-496 | Erdős Problem #496: Number Theory, Diophantine Approximation | Let $\alpha \in \mathbb{R}$ be irrational and $\epsilon>0$. Are there positive integers $x,y,z$ such that\[\lvert x^2+y^2-z^2\alpha\rvert <\epsilon?\] | Erdős Problems (#496, https://www.erdosproblems.com/496). 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/496",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"diophantine-approximation"
] | null | null | null | null | https://www.erdosproblems.com/496 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,903 | EP-497 | Erdős Problem #497: Combinatorics | How many antichains in $[n]$ are there? That is, how many families of subsets of $[n]$ are there such that, if $\mathcal{F}$ is such a family and $A,B\in \mathcal{F}$, then $A\not\subseteq B$? | Erdős Problems (#497, https://www.erdosproblems.com/497). Maintainer status: SOLVED (LEAN). Dedekind's problem OEIS: A000372. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.497). | 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/497",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | Dedekind's problem | [
"erdos-problems",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/497 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,904 | EP-498 | Erdős Problem #498: Combinatorics, Analysis | Let $z_1,\ldots,z_n\in\mathbb{C}$ with $1\leq \lvert z_i\rvert$ for $1\leq i\leq n$. Let $D$ be an arbitrary disc of radius $1$. Is it true that the number of sums of the shape\[\sum_{i=1}^n\epsilon_iz_i \textrm{ for }\epsilon_i\in \{-1,1\}\]which lie in $D$ is at most $\binom{n}{\lfloor n/2\rfloor}$? | Erdős Problems (#498, https://www.erdosproblems.com/498). Maintainer status: PROVED (LEAN). strong Littlewood-Offord problem Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.498). | 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/498",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | strong Littlewood-Offord problem | [
"erdos-problems",
"combinatorics",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/498 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,905 | EP-499 | Erdős Problem #499: Combinatorics | Let $M=(a_{ij})$ be a real $n\times n$ doubly stochastic matrix (i.e. the entries are non-negative and each column and row sums to $1$). Does there exist some $\sigma\in S_n$ such that\[\prod_{1\leq i\leq n}a_{i\sigma(i)}\geq n^{-n}?\] | Erdős Problems (#499, https://www.erdosproblems.com/499). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.499). | 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/499",
"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/499 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,906 | EP-502 | Erdős Problem #502: Geometry, Distances | What is the size of the largest $A\subseteq \mathbb{R}^n$ such that there are only two distinct distances between elements of $A$? That is,\[\# \{ \lvert x-y\rvert: x\neq y\in A\} = 2.\] | Erdős Problems (#502, https://www.erdosproblems.com/502). Maintainer status: SOLVED (LEAN). OEIS: A027627. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.502). | 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/502",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/502 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,907 | EP-504 | Erdős Problem #504: Geometry | Let $\alpha_n$ be the supremum of all $0\leq \alpha\leq \pi$ such that in every set $A\subset \mathbb{R}^2$ of size $n$ there exist three distinct points $x,y,z\in A$ such that the angle determined by $xyz$ is at least $\alpha$. Determine $\alpha_n$. | Erdős Problems (#504, https://www.erdosproblems.com/504). Maintainer status: SOLVED. Blumenthal's problem | 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/504",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved"
} | null | null | null | Blumenthal's problem | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/504 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,908 | EP-505 | Erdős Problem #505: Geometry | Is every set of diameter $1$ in $\mathbb{R}^n$ the union of at most $n+1$ sets of diameter $<1$? | Erdős Problems (#505, https://www.erdosproblems.com/505). Maintainer status: DISPROVED (LEAN). Borsuk's problem Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.505). | 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... | [
"GEO-029",
"AMR-112-0001"
] | {
"source_url": "https://www.erdosproblems.com/505",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | Borsuk's problem | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/505 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,909 | EP-506 | Erdős Problem #506: Geometry | What is the minimum number of circles determined by any $n$ points in $\mathbb{R}^2$, not all on a circle? | Erdős Problems (#506, https://www.erdosproblems.com/506). Maintainer status: DECIDABLE. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.506). | 3 | open | Paul Erdős | null | 6 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/506",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "decidable"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/506 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,910 | EP-511 | Erdős Problem #511: Analysis | Let $f(z)\in \mathbb{C}[z]$ be a monic polynomial of degree $n$. Is it true that, for every $c>1$, the set\[\{ z\in \mathbb{C}: \lvert f(z)\rvert< 1\}\]has at most $O_c(1)$ many connected components of diameter $>c$ (where the implied constant is in particular independent of $n$)? | Erdős Problems (#511, https://www.erdosproblems.com/511). Maintainer status: DISPROVED. | 3 | solved | Paul Erdős | null | 8 | 8 | 0 | 0 | 2026-10-16T14:00:00 | 2026-10-16T14:00:00 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/511",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/511 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,911 | EP-512 | Erdős Problem #512: Analysis | Is it true that, if $A\subset \mathbb{Z}$ is a finite set of size $N$, then\[\int_0^1 \left\lvert \sum_{n\in A}e(n\theta)\right\rvert \mathrm{d}\theta \gg \log N,\]where $e(x)=e^{2\pi ix }$? | Erdős Problems (#512, https://www.erdosproblems.com/512). Maintainer status: PROVED (LEAN). Littlewood's conjecture Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.512). | 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/512",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | Littlewood's conjecture | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/512 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,912 | EP-515 | Erdős Problem #515: Analysis | Let $f(z)$ be an entire function, not a polynomial. Does there exist a locally rectifiable path $C$ tending to infinity such that, for every $\lambda>0$, the integral\[\int_C \lvert f(z)\rvert^{-\lambda} \mathrm{d}z\]is finite? | Erdős Problems (#515, https://www.erdosproblems.com/515). 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/515",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved"
} | null | null | null | null | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/515 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,913 | EP-516 | Erdős Problem #516: Analysis | Let $f(z)=\sum_{k\geq 1}a_k z^{n_k}$ be an entire function of finite order such that $\lim n_k/k=\infty$. Let $M(r)=\max_{\lvert z\rvert=r}\lvert f(z)\rvert$ and $m(r)=\min_{\lvert z\rvert=r}\lvert f(z)\rvert$. Is it true that\[\limsup\frac{\log m(r)}{\log M(r)}=1?\] | Erdős Problems (#516, https://www.erdosproblems.com/516). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.516). | 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/516",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/516 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,914 | EP-518 | Erdős Problem #518: Graph Theory, Ramsey Theory | Is it true that, in any two-colouring of the edges of $K_n$, there exist $\sqrt{n}$ monochromatic paths, all of the same colour, which cover all vertices? | Erdős Problems (#518, https://www.erdosproblems.com/518). 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/518",
"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/518 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
30,006,915 | EP-519 | Erdős Problem #519: Analysis | Let $z_1,\ldots,z_n\in \mathbb{C}$ with $z_1=1$. Must there exist an absolute constant $c>0$ such that\[\max_{1\leq k\leq n}\left\lvert \sum_{i}z_i^k\right\rvert>c?\] | Erdős Problems (#519, https://www.erdosproblems.com/519). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.519). | 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/519",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/519 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
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