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Erdős Problem #123

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

2 comments

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?

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No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    GPT-5.6, with Colin Snyder

    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.

    AI involvement
    ai discovered
    — the result was found by a model.

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

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

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

    Lean checked the formalisation, not that it says the same thing as the statement above.

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