Erdős Problems

1,217 source-owned questions · 604 with a formal statement · searchable by statement, number, topic and source status.

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1,217 Problems · 2 with reviewed evidence

26/26

Number	Question	Source says	Formal	Result here
#1201	Is it true that for every $\epsilon,\eta>0$ there exists a $k$ such that the density of $n$ for which $P(n(n+1)\cdots(n+k))>n^{1-\epsilon}$ is at least $1-\eta$ (where $P(m)$ is the greatest prime divisor of $m$ )?openFormalized	open	In Lean	No Result decision
#1202	No statement retained — open to read what the source holdssolvedNo formal declaration	solved	No formal statement	No Result decision
#1203	Prove that $F(n)\to \infty$ as $n\to \infty$ .openFormalized	open	In Lean	No Result decision
#1204	No statement retained — open to read what the source holdsopenNo formal declaration	open	No formal statement	No Result decision
#1205	No statement retained — open to read what the source holdssolvedNo formal declaration	solved	No formal statement	No Result decision
#1206	No statement retained — open to read what the source holdsopenNo formal declaration	open	No formal statement	No Result decision
#1207	No statement retained — open to read what the source holdsopenNo formal declaration	open	No formal statement	No Result decision
#1208	No statement retained — open to read what the source holdsopenNo formal declaration	open	No formal statement	No Result decision
#1209	Let $A=\{a_1<a_2<\cdots\}$ be a sequence of integers which tends to infinity sufficiently fast. If there is an $n$ such that all $n+a_k$ are primes then must there exist infinitely many such $n$ ?openFormalized	open	In Lean	No Result decision
#1210	Let $A\subseteq [1,n)$ be a set of integers such that $(a,b)=1$ for all distinct $a,b\in A$ . Is it true that $\sum_{a\in A}\frac{1}{n-a}\leq \sum_{p < n}\frac{1}{p}+O(1)$ ?openFormalized	open	In Lean	No Result decision
#1211	No statement retained — open to read what the source holdssolvedNo formal declaration	solved	No formal statement	No Result decision
#1212	Roughness criterion (sufficiency for the anchor conditions): if $a < s$ for all $s$ in the leg and the leg stays below $a + P^-(a)$ , then $a$ is coprime to the whole leg. Stated via divisibility: no prime factor of $a$ divides any $s$ with $a < s < a + p$ for all prime factors $p$ of $a$ .openFormalized	open	In Lean	No Result decision
#1213	No statement retained — open to read what the source holdsprovedNo formal declaration	proved	No formal statement	No Result decision
#1214	Let $x,y\geq 1$ be integers such that, for all $n\geq 1$ , the set of primes dividing $x^{n}-1$ is equal to the set of primes dividing $y^n-1$ . Must $x=y$ ?provedFormalized	proved	In Lean	No Result decision
#1215	No statement retained — open to read what the source holdsdisprovedNo formal declaration	disproved	No formal statement	No Result decision
#1216	No statement retained — open to read what the source holdsdisprovedNo formal declaration	disproved	No formal statement	No Result decision
#1217	No statement retained — open to read what the source holdsprovedNo formal declaration	proved	No formal statement	No Result decision

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