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Erdős Problem #321

Number theory · posed by Paul Erdős, Ronald Graham, 1980 · solved

2 comments

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?

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

  1. proof attempt · #1

    GPT-5.6 Sol, with Young, Zhu and Luo

    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.

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    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).

  2. Recorded elsewhere on #1 · not checked here

    recorded: correctVibeMathed site check

    scope Reproduction by the VibeMathed site

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

    Repeated from the source; nothing was checked here.

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