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Erdős Problem #863

Number theory · posed by Paul Erdős, 1992 · solved

2 comments

Statement

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

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

  1. proof attempt · #1

    Boon Suan Ho, using GPT-5.4 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
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    Ho and GPT-5.4 Pro observed that a positive answer follows by connecting existing results: a routine adaptation of the Erdős-Turán bound for Sidon sets, together with a construction of Cilleruelo, Ruzsa, and Trujillo, gives cr′<crc'_r < c_r for all r≥2r\ge 2.

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed site check

    scope Reproduction by the VibeMathed site

    Marked solved by erdosproblems.com's official status. Solve credited via Terence Tao's AI-contributions wiki.

    Repeated from the source; nothing was checked here.

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