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Erdős Problem #769

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erdos-769Geometry & topologyposer not recordedrecorded: partial

1 attempt · 1 machine check · no person has looked

Statement

For the least cutoff c(n)c(n) after which every kk occurs as the number of homothetic cubes in a decomposition of the unit nn-cube, is c(n)≫nnc(n) \gg n^n? The Lean proof shows c(n)=o(nn)c(n) = o(n^n) along odd dimensions.

Context

the conjectured lower bound is disproved; good bounds for c(n) remain open

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.

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Interest

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Attempts

1 attempt

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  • #1

    Attempt 1

    constructionGPT-5.6 starships (Claude Fable 5 reviewer) ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.6 starships (Claude Fable 5 reviewer)

    Produced by the GPT-5.6 starships pipeline with Claude Fable 5 as reviewer.

    the conjectured lower bound is disproved; good bounds for c(n) remain open

    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 Lean ·

      scope Lean formalization of the result

      Lean-checked; community status pending.

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    Discussion of this attempt

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Discussion

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