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The Erdos-Graham Semiprime Unit Fraction Problem

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erdos-graham-semiprime-unit-fractionsNumber theoryposed by Paul Erdos, Ronald Graham, 2015recorded: solved

1 attempt · no person has looked

Statement

Every natural number is a finite sum of distinct unit fractions whose denominators are semiprimes. This is the ω=2\omega = 2 integer case of a problem of Erdos and Graham, left as a conjecture by Butler, Erdos and Graham, who proved the ω=3\omega = 3 analogue.

Context

the omega = 2 integer case, the one Butler, Erdos and Graham left open

A stated conjecture from the Butler-Erdos-Graham unit fractions paper, in the Erdos-Graham problem tradition.

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1 attempt

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  • #1

    Attempt 1

    proof attemptClaude (via Claude Code) with Shisheng Li ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    Claude (via Claude Code)
    people
    Shisheng Li

    The paper describes itself as a human-AI collaboration and says the tools contributed substantially to the Lean formalisation.

    the omega = 2 integer case, the one Butler, Erdos and Graham left open

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