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Erdős Problem #793

Number theory · posed by Paul Erdős, 1969 · solved

2 comments

Statement

Let F(n)F(n) be the largest A⊆{1,…,n}A\subseteq\{1,\dots,n\} with a∤bca\nmid bc for distinct a,b,c∈Aa,b,c\in A. Is F(n)=π(n)+(C+o(1)) n2/3(log⁡n)−2F(n)=\pi(n)+(C+o(1))\,n^{2/3}(\log n)^{-2} for some constant CC?

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    GPT-5.6 Sol, with Przemek Chojecki

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    GPT-5.6 Sol (prompted by Przemek Chojecki) proved F(n)=π(n)+(272+o(1))n2/3(log⁡n)2F(n)=\pi(n)+(\tfrac{27}{2}+o(1))\frac{n^{2/3}}{(\log n)^2}, a refined form of Erdős's 1938 argument.

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed site check

    scope Reproduction by the VibeMathed site

    Marked proved on erdosproblems.com via a proof claim by GPT-5.6 Sol; not formally Lean-verified.

    Repeated from the source; nothing was checked here.

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