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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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  • 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

16 Problems

SelectNumberQuestionOpen
#67The Erdős discrepancy problemSource says provedFormalized
#161No statement retained — open to read what the source holdsSource says openNo formal declaration
#162No statement retained — open to read what the source holdsSource says openNo formal declaration
#176No statement retained — open to read what the source holdsSource says openNo formal declaration
#177No statement retained — open to read what the source holdsSource says openNo formal declaration
#178Let A1,A2,…A_1,A_2,\ldots be an infinite collection of infinite sets of integers, say Ai={ai1<ai2<⋯ }A_i=\{a_{i1}<a_{i2}<\cdots\}. Does there exist some f:N→{−1,1}f:\mathbb{N}\to\{-1,1\} such that max⁡m,1≤i≤d∣∑1≤j≤mf(aij)∣≪d1\max_{m, 1\leq i\leq d} \left\lvert \sum_{1\leq j\leq m} f(a_{ij})\right\rvert \ll_d 1 for all d≥1d\geq 1?Source says proved (Lean)Formalized
#255No statement retained — open to read what the source holdsSource says provedNo formal declaration
#987Question 1:Source says provedFormalized
#988No statement retained — open to read what the source holdsSource says solvedNo formal declaration
#989No statement retained — open to read what the source holdsSource says solvedNo formal declaration
#991No statement retained — open to read what the source holdsSource says provedNo formal declaration
#992No statement retained — open to read what the source holdsSource says disprovedNo formal declaration
#994No statement retained — open to read what the source holdsSource says disprovedNo formal declaration
#995No statement retained — open to read what the source holdsSource says openNo formal declaration
#997Is it true that, for every α\alpha, the sequence {αpn}\{ \alpha p_n\} is not well-distributed, if pnp_n is the sequence of primes?Source says proved (Lean)Formalized
#1028Let H(n)=min⁡fmax⁡X⊆{1,…,n}∣∑x<y∈Xf(x,y)∣,H(n)=\min_f \max_{X\subseteq \{1,\ldots,n\}} \left\lvert \sum_{x<y\in X} f(x,y)\right\rvert, where ff ranges over all functions f:{1,…,n}2→{−1,1}f:\{1,\ldots,n\}^2\to \{-1,1\}. Estimate H(n)H(n).Source says solved (Lean)Formalized