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Erdős problem 650

Let f(m)f(m) be such that if A⊆{1,…,N}A\subseteq \{1,\ldots,N\} has ∣A∣=m\lvert A\rvert=m then every interval in [1,∞)[1,\infty) of length 2N2N contains ≥f(m)\geq f(m) many distinct integers b1,…,brb_1,\ldots,b_r where each bib_i is divisible by some ai∈Aa_i\in A, where a1,…,ara_1,\ldots,a_r are distinct.

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Retained declaration

FormalConjectures/ErdosProblems/650.lean

Formal Conjectures

FormalConjectures/ErdosProblems/650.leanErdos650.erdos_650.parts.i1 lineExact file
∀ (m : ℕ), Erdos650.f m = min m ⌈2 * √↑m⌉₊
SolvedStatement only, no proof

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:650
  • PLBY Lean proofsErdosProblems.Erdos650

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

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