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Erdős Problem #123

Number theory · posed by Paul Erdős, Mordechai Lewin, 1996 · solved

1 attempt · 1 machine check

Statement

Let a,b,c>1a,b,c>1 be pairwise coprime integers. Is every large integer a sum of distinct numbers of the form akblcma^k b^l c^m (k,l,m≥0k,l,m\ge 0), none dividing another?

Context

A numbered Erdos problem that an unusually dense reference trail on erdosproblems.com (6 sources), setting it above the typical entry in the catalog.

People

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Attempts

1 attempt

No person has examined this. There is 1 attempt here and 1 machine check recorded against it. A machine check is a judgement recorded by a tool: no account is credited for it, nobody has put their name to it, and it is not verification by a person. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

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  • #1

    Attempt 1

    proof attemptGPT-5.6 with Colin Snyder ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.6
    people
    Colin Snyder

    GPT-5.6 (prompted by Colin Snyder) resolved the Erdős-Lewin conjecture in the affirmative.

    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 Lean ·

      scope Lean formalization of the result

      Marked proved (Lean) on erdosproblems.com; carried an Erdős prize of USD 250. Formally verified in Lean.

      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.

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