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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

8 Problems

SelectNumberQuestionOpen
#343No statement retained — open to read what the source holdsSource says provedNo formal declaration
#344No statement retained — open to read what the source holdsSource says provedNo formal declaration
#345No statement retained — open to read what the source holdsSource says openNo formal declaration
#346Is it true that for every lacunary, strongly complete sequence A that is not complete whenever infinitely many terms are removed from it, lim A (n + 1) / A n = (1 + √5) / 2?Source says openFormalized
#347Is there a sequence A={a1≤a2≤⋯ }A=\{a_1\leq a_2\leq \cdots\} of integers with lim⁡an+1an=2\lim \frac{a_{n+1}}{a_n}=2 such that P(A′)={∑n∈Bn:B⊆A′ finite }P(A')= \left\{\sum_{n\in B}n : B\subseteq A'\textrm{ finite }\right\} has density 11 for every cofinite subsequence A′A' of AA?Source says proved (Lean)Formalized
#348For what values of 0≤m<n0 \leq m < n is there a complete sequence A={a1≤a2≤⋯ }A = \{a_1 \leq a_2 \leq \cdots\} of integers such that 1. AA remains complete after removing any mm elements, but 2. AA is not complete after removing any nn elements.Source says openFormalized
#349For α>2\alpha > 2 and any t>0t > 0, the sequence ⌊tαn⌋\lfloor t\alpha^n\rfloor is not additively complete; equivalently (t,α)(t, \alpha) is not a "good pair". A partial result on the open Erdős Problem 349: it complements complete_for_alpha_in_Ioo_one_to_goldenRatio.Source says openFormalized
#351Let p(x)∈Q[x]p(x) \in \mathbb{Q}[x] be a non-constant rational polynomial with positive leading coefficient. Is it true that A={p(n)+1/n:n∈N}A=\{ p(n)+1/n : n \in \mathbb{N}\} is strongly complete, in the sense that, for any finite set BB, {∑a∈Xa:X⊆A∖B,X is finite}\left\{\sum_{a \in X} a : X \subseteq A \setminus B, X \textrm{ is finite}\right\} contains all sufficiently large integers?Source says proved (Lean)Formalized