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Erdos Problem #731

Number theory · posed by Paul Erdos · partial

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Statement

Let A(n)A(n) be the least positive integer not dividing (2nn)\binom{2n}{n}. Erdos asked for the behaviour of A(n)A(n) for reasonable nn. Under an explicit dyadic-regularity formalization of reasonable, the distribution is determined on dyadic intervals against the scale FX=2(log⁡2)1/4L1/4exp⁡(log⁡2)LF_X = \sqrt{2}(\log 2)^{1/4} L^{1/4} \exp\sqrt{(\log 2)L} with L=log⁡(2X)L = \log(2X).

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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
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    The declaration says large language models, primarily ChatGPT, were used extensively throughout the research while the author originated the ideas, and that the accompanying Lean formalization was developed by the author with Aristotle.

    resolved under an explicit formalization of 'reasonable', not in full generality

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