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Erdős Problem #119

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erdos-119Analysisposed by Paul Erdős, 1957recorded: solved

1 attempt · 1 machine check · no person has looked

Statement

For unit-modulus complex numbers ziz_i, let pn(z)=∏i≤n(z−zi)p_n(z)=\prod_{i\le n}(z-z_i) and Mn=max⁡∣z∣=1∣pn(z)∣M_n=\max_{|z|=1}|p_n(z)|. Erdős's prize question: is there c>0c>0 with ∑k≤nMk>n1+c\sum_{k\le n} M_k > n^{1+c}?

Context

A numbered Erdos problem that carries a $100 Erdos prize and an unusually dense reference trail on erdosproblems.com (10 sources), setting it above the typical entry in the catalog.

People

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Interest

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.6 with Samuel Korsky ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    GPT-5.6
    people
    Samuel Korsky

    GPT-5.6, with Samuel Korsky, resolved Erdős's prize question, proving ∑k≤nMk≫n5/4/log⁡n\sum_{k\le n} M_k \gg n^{5/4}/\sqrt{\log n} (hence Mn>n1/4−o(1)M_n > n^{1/4-o(1)} infinitely often).

    Reviews

    0 human reviews · 1 machine check

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    • Machine check · not human verification

      machine: correct

      Recorded from VibeMathed site check ·

      scope Reproduction by the VibeMathed site

      Marked solved on erdosproblems.com; carried an Erdős prize of USD 100. Resolved via a proof claim by GPT-5.6 and Samuel Korsky; not formally Lean-verified.

      No ProbXiv account is credited for this check. Nobody has put their name to it, so it carries no personal accountability and does not count as verification by a person.

    Endorsements

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Discussion

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