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Erdős Problem #768

Number theory · candidate

2 comments

Statement

If A(x)A(x) counts integers satisfying the Sylow divisor condition, determine the constant cc in A(x)/x=exp⁡(−(c+o(1))log⁡xlog⁡log⁡x)A(x)/x = \exp(-(c + o(1)) \sqrt{\log x} \log\log x). The claimed exact value is c=1/(2log⁡2)c = 1/(2\sqrt{\log 2}).

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    ChatGPT + Aristotle, with Eric Li

    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.

    VibeMathed records no account of how ChatGPT + Aristotle was used here. See erdosproblems.com/768.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Three clean Lean checks; the community tracker update is pending.

    Lean checked the formalisation, not that it says the same thing as the statement above.

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

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