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Erdős Problems

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

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Source status, exact formal material, and reviewed Results are separate signals.

  • Open per source608
  • Resolved per source556
  • Other source status53
Exact formal statement available604 / 1,217
With Repository-reviewed evidence2 / 1,217
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Problems

1,217 Problems · 2 with reviewed evidence

25/26

NumberQuestionOpen
#1153No statement retained — open to read what the source holdsprovedNo formal declaration
#1154No statement retained — open to read what the source holdsnot disprovableNo formal declaration
#1155No statement retained — open to read what the source holdsopenNo formal declaration
#1156No statement retained — open to read what the source holdsopenNo formal declaration
#1157No statement retained — open to read what the source holdsopenNo formal declaration
#1158No statement retained — open to read what the source holdsopenNo formal declaration
#1159No statement retained — open to read what the source holdsopenNo formal declaration
#1160No statement retained — open to read what the source holdsopenNo formal declaration
#1161No statement retained — open to read what the source holdssolvedNo formal declaration
#1162No statement retained — open to read what the source holdsopenNo formal declaration
#1163No statement retained — open to read what the source holdsopenNo formal declaration
#1164No statement retained — open to read what the source holdsprovedNo formal declaration
#1165No statement retained — open to read what the source holdssolvedNo formal declaration
#1166No statement retained — open to read what the source holdsprovedNo formal declaration
#1167The partition relation μ→(ν)1r\mu \to (\nu)^r_1 with a single color is equivalent to ν≤μ\nu \le \mu.openFormalized
#1168No statement retained — open to read what the source holdsopenNo formal declaration
#1169No statement retained — open to read what the source holdsnot disprovableNo formal declaration
#1170No statement retained — open to read what the source holdsopenNo formal declaration
#1171No statement retained — open to read what the source holdsopenNo formal declaration
#1172No statement retained — open to read what the source holdsopenNo formal declaration
#1173No statement retained — open to read what the source holdsopenNo formal declaration
#1174No statement retained — open to read what the source holdsnot disprovableNo formal declaration
#1175Let κ\kappa be an uncountable cardinal. Must there exist a cardinal λ\lambda such that every graph with chromatic number λ\lambda contains a triangle-free subgraph with chromatic number κ\kappa?openFormalized
#1176Let GG be a graph with chromatic number ℵ1\aleph_1. Is it true that there is a colouring of the edges with ℵ1\aleph_1 many colours such that, in any countable colouring of the vertices, there exists a vertex colour containing all edge colours?not disprovableFormalized
#1177No statement retained — open to read what the source holdsopenNo formal declaration
#1178No statement retained — open to read what the source holdsopenNo formal declaration
#1179No statement retained — open to read what the source holdsprovedNo formal declaration
#1180No statement retained — open to read what the source holdsprovedNo formal declaration
#1181No statement retained — open to read what the source holdsopenNo formal declaration
#1182No statement retained — open to read what the source holdsopenNo formal declaration
#1183No statement retained — open to read what the source holdsopenNo formal declaration
#1184No statement retained — open to read what the source holdsopenNo formal declaration
#1185No statement retained — open to read what the source holdssolvedNo formal declaration
#1186No statement retained — open to read what the source holdsopenNo formal declaration
#1187No statement retained — open to read what the source holdssolvedNo formal declaration
#1188Call a set of distinct integers 1<n1<⋯<nk1<n_1<\cdots<n_k with associated congruence classes ai(modni)a_i\pmod{n_i} a distinct covering system if every integer satisfies at least one of these congruences. A minimal distinct covering system is one such that no proper subset forms a covering system. Let F(x)F(x) count the number of minimal distinct covering systems with all moduli in [1,x][1,x]. Estimate F(x)F(x).openFormalized
#1189No statement retained — open to read what the source holdsopenNo formal declaration
#1190Let ϵm=max⁡∑1ni\epsilon_m=\max \sum \frac{1}{n_i} where the maximum is taken over all finite sequences m<n1<⋯<nkm<n_1<\cdots<n_k for which there exist congruences ai(modni)a_i\pmod{n_i} such that no integer satisfies two such congruences.solved (Lean)Formalized
#1191No statement retained — open to read what the source holdsopenNo formal declaration
#1192Does there exist, for all r≥2r\geq 2, a basis AA of order rr (so that fr(n)>0f_r(n)>0 for all large nn) such that ∑n≤xfr(n)2≪x\sum_{n\leq x}f_r(n)^2 \ll x for all xx?openFormalized
#1193Let A⊂NA\subset \mathbb{N} and let g(n)g(n) be a non-decreasing function of nn which is always >0>0.solved (Lean)Formalized
#1194No statement retained — open to read what the source holdsopenNo formal declaration
#1195No statement retained — open to read what the source holdssolvedNo formal declaration
#1196Is it true that, for any xx, if A⊂[x,∞)A\subset [x,\infty) is a primitive set of integers (so that no distinct elements of AA divide each other) then\sum_{a\in A}\frac{1}{a\log a}&#60; 1+o(1),where the o(1)o(1) term →0\to 0 as x→∞x\to \infty? -proved (Lean)Formalized
#1197No statement retained — open to read what the source holdsdisproved (Lean)No formal declaration
#1198No statement retained — open to read what the source holdsdisprovedNo formal declaration
#1199Is it true that in any 2-colouring of N\mathbb{N} there exists an infinite set AA such that all elements of A+AA+A are the same colour?openFormalized
#1200No statement retained — open to read what the source holdsopenNo formal declaration

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