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Erdos Problem #768

Number theory · posed by Paul Erdos · solved

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Statement

Let A(x)A(x) count n≤xn \le x such that every prime p∣np \mid n has a divisor d>1d > 1 of nn with d≡1(modp)d \equiv 1 \pmod p. Erdos asked whether A(x)/x=exp⁡(−(c+o(1))log⁡xlog⁡log⁡x)A(x)/x = \exp(-(c+o(1))\sqrt{\log x}\log\log x). It does, with c=1/(2log⁡2)c = 1/(2\sqrt{\log 2}).

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

  1. proof attempt · #1

    Eric Li, using ChatGPT, Aristotle

    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
    — a person and a model developed the result together.

    The declaration says large language models, primarily ChatGPT, were used extensively throughout the research, with the author originating the ideas, and that the accompanying Lean formalization was produced with Harmonic's Aristotle under the author's direction and audit. The author also notes rejecting flawed model suggestions along the way.

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open in Claude →open in ChatGPT →

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