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Erdős Problem #1189

Number theory · partial

2 comments

Statement

For irreducible covering sets of size kk, determine their count, the possible largest modulus, the maximal reciprocal sum, and whether divisor-set examples occur infinitely often.

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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 Star Fleet (Claude Fable 5 referee)

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

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

    exact largest modulus 3·2^{k-3} for k ≥ 5, near-linear least maximum, reciprocal mass Θ(log k), and an infinite divisor family; the counting asymptotic rests on the cited BBMST theorem

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

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked with one named literature input made explicit; community status pending.

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

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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

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