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The Umans-Wang Arithmetic-Progression Divisor Conjecture

Number theory · posed by Chris Umans, Sheng Wang, 2025 · disproved

1 comment

Statement

An nn-divisor set contains a multiple of every integer from 1 to nn. Umans and Wang proposed, as the arithmetic-progression form of their Strong (α,β)(\alpha,\beta)-Divisor Conjecture, that such a progression exists with few terms of bounded magnitude, which would imply faster algorithms for polynomial and integer factorization. Refuted unconditionally, including its exponent-level relaxation.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    GPT-5.6 Sol (via Codex, reasoning effort ultra), with Xinjie He and Amit Sahai

    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.

    "The proof was discovered in an OpenAI Codex run using the gpt-5.6-sol model with reasoning effort set to ultra. Codex also produced the initial write-up. Subsequent human review verified the proof, reviewed the citations, and revised the exposition." The authors note the prompting strategy borrowed from the UCLA Moonshot Harness project.

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