Erdős Problems

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

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With Repository-reviewed evidence2 / 1,217

1,217 Problems · 2 with reviewed evidence

12/26

Number	Question	Source says	Formal	Result here
#529	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#530	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#531	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#532	If $\mathbb{N}$ is 2-coloured then is there some infinite set $A\subseteq \mathbb{N}$ such that all finite subset sums $\sum_{n\in S}n$ (as $S$ ranges over all non-empty finite subsets of $A$ ) are monochromatic?Source says proved (Lean)Formalized	proved (Lean)	In Lean	No Result decision
#533	Let $\delta > 0$ . If $n$ is sufficiently large and $G$ is a graph on $n$ vertices with no $K_5$ and at least $\delta n^2$ edges, must $G$ contain a set of $\gg_\delta n$ vertices spanning no triangle?Source says disprovedFormalized	disproved	In Lean	No Result decision
#534	No statement retained — open to read what the source holdsSource says solvedNo formal declaration	solved	No formal statement	No Result decision
#535	Let $r \geq 3$ , and let $f_r(N)$ denote the size of the largest subset of $\{1,\ldots,N\}$ such that no subset of size $r$ has the same pairwise greatest common divisor between all elements. Erdős [Er64] proved that $f_3(N) > N^{c/\log\log N}$ for some constant $c > 0$ , and conjectured this should also be an upper bound; here we state the conjectural upper bound for all $r \geq 3$ .Source says openFormalized	open	In Lean	No Result decision
#536	Let $\epsilon>0$ and $N$ be sufficiently large. Is it true that if $A\subseteq \{1,\ldots,N\}$ has size at least $\epsilon N$ then there must be distinct $a,b,c\in A$ such that $[a, b]=[b, c]=[a, c],$ where $[\cdot, \cdot]$ denotes the least common multiple?Source says openFormalized	open	In Lean	No Result decision
#537	Let $\epsilon>0$ and $N$ be sufficiently large. If $A\subseteq \{1,\ldots,N\}$ has $\lvert A\rvert \geq \epsilon N$ then must there exist $a_1,a_2,a_3\in A$ and distinct primes $p_1,p_2,p_3$ such that $a_1p_1=a_2p_2=a_3p_3?$ Source says disproved (Lean)Formalized	disproved (Lean)	In Lean	No Result decision
#538	Let $r\geq 2$ and suppose that $A\subseteq\{1,\ldots,N\}$ is such that, for any $m$ , there are at most $r$ solutions to $m=pa$ where $p$ is prime and $a\in A$ . Give the best possible upper bound for $\sum_{n\in A}\frac{1}{n}$ .Source says openFormalized	open	In Lean	No Result decision
#539	Let $h(n)$ be maximal such that, for any set $A\subseteq \mathbb{N}$ of size $n$ , the set $\left\{ \frac{a}{(a,b)}: a,b\in A\right\}$ has size at least $h(n)$ . Estimate $h(n)$ .Source says openFormalized	open	In Lean	No Result decision
#540	Is it true that if $A\subseteq \mathbb{Z}/N\mathbb{Z}$ has size $\gg N^{1/2}$ then there exists some non-empty $S\subseteq A$ such that $\sum_{n\in S}n\equiv 0\pmod{N}$ ?Source says proved (Lean)Formalized	proved (Lean)	In Lean	No Result decision
#541	Let $a_1, \dots, a_p$ be (not necessarily distinct) residues modulo a prime $p$ , such that there exists some $r$ so that if $S \subseteq [p]$ is non-empty and $\sum_{i \in S} a_i \equiv 0 \pmod{p}$ then $\|S\| = r$ .Source says proved (Lean)Formalized	proved (Lean)	In Lean	No Result decision
#542	No statement retained — open to read what the source holdsSource says solvedNo formal declaration	solved	No formal statement	No Result decision
#543	No statement retained — open to read what the source holdsSource says disprovedNo formal declaration	disproved	No formal statement	No Result decision
#544	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#545	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#546	No statement retained — open to read what the source holdsSource says provedNo formal declaration	proved	No formal statement	No Result decision
#547	No statement retained — open to read what the source holdsSource says decidableNo formal declaration	decidable	No formal statement	No Result decision
#548	No statement retained — open to read what the source holdsSource says falsifiableNo formal declaration	falsifiable	No formal statement	No Result decision
#549	No statement retained — open to read what the source holdsSource says disprovedNo formal declaration	disproved	No formal statement	No Result decision
#550	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#551	No statement retained — open to read what the source holdsSource says decidableNo formal declaration	decidable	No formal statement	No Result decision
#552	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#553	No statement retained — open to read what the source holdsSource says provedNo formal declaration	proved	No formal statement	No Result decision
#554	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#555	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#556	No statement retained — open to read what the source holdsSource says decidableNo formal declaration	decidable	No formal statement	No Result decision
#557	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#558	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#559	No statement retained — open to read what the source holdsSource says disprovedNo formal declaration	disproved	No formal statement	No Result decision
#560	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#561	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#562	Let $R_r(n)$ denote the $r$ -uniform hypergraph Ramsey number: the minimal $m$ such that if we $2$ -colour all edges of the complete $r$ -uniform hypergraph on $m$ vertices then there must be some monochromatic copy of the complete $r$ -uniform hypergraph on $n$ vertices.Source says openFormalized	open	In Lean	No Result decision
#563	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#564	Let $R_3(n)$ be the minimal $m$ such that if the edges of the $3$ -uniform hypergraph on $m$ vertices are $2$ -coloured then there is a monochromatic copy of the complete $3$ -uniform hypergraph on $n$ vertices.Source says openFormalized	open	In Lean	No Result decision
#565	No statement retained — open to read what the source holdsSource says provedNo formal declaration	proved	No formal statement	No Result decision
#566	Let $G$ be such that any subgraph on $k$ vertices has at most $2k-3$ edges. Is it true that, if $H$ has $m$ edges and no isolated vertices, then $\hat{r}(G,H) \ll m$ ?Source says openFormalized	open	In Lean	No Result decision
#567	Erdős Problem 567 (Q3)Source says openFormalized	open	In Lean	No Result decision
#568	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#569	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#570	No statement retained — open to read what the source holdsSource says provedNo formal declaration	proved	No formal statement	No Result decision
#571	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#572	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#573	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#574	No statement retained — open to read what the source holdsSource says disprovedNo formal declaration	disproved	No formal statement	No Result decision
#575	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision
#576	No statement retained — open to read what the source holdsSource says openNo formal declaration	open	No formal statement	No Result decision