The Umans-Wang Arithmetic-Progression Divisor Conjecture
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Statement
An -divisor set contains a multiple of every integer from 1 to . Umans and Wang proposed, as the arithmetic-progression form of their Strong -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.
Context
A 2025 conjecture whose truth would have implied faster polynomial and integer factorization, so it carried real algorithmic stakes; young, but posed by Umans and pursued for that consequence.
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"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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0 human reviews · 0 machine checksNo person has reviewed this attempt. It has not been checked at all.
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