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Erdős Problem #321

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erdos-321Number theoryposed by Paul Erdős, Ronald Graham, 1980recorded: solved

1 attempt · 1 machine check · no person has looked

Statement

What is the largest A⊆{1,…,N}A\subseteq\{1,\dots,N\} such that all subset sums ∑n∈S1/n\sum_{n\in S}1/n (over S⊆AS\subseteq A) are distinct?

Context

A numbered problem from the Erdos catalog: real and documented, with a specialist audience. Checked against erdosproblems.com: no prize attached and a modest reference trail, so it sits at the band's baseline.

People

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Projects

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Interest

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptGPT-5.6 Sol with Young, Zhu, Luo ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.6 Sol
    people
    Young, Zhu, Luo

    GPT-5.6 Sol (prompted by Young, Zhu, and Luo) proved the matching upper bound R(N)≍Nlog⁡N∏j≥3log⁡jNR(N)\asymp \frac{N}{\log N}\prod_{j\ge 3}\log_j N (companion to #320).

    Reviews

    0 human reviews · 1 machine check

    No person has reviewed this attempt. 1 machine check below — a machine check is not human verification.

    • Machine check · not human verification

      machine: correct

      Recorded from VibeMathed site check ·

      scope Reproduction by the VibeMathed site

      Marked solved on erdosproblems.com via a proof claim; follows from the resolution of #320.

      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 of this attempt

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Discussion

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