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Erdős Problem #728: Factorial Divisibility

Whether there are infinitely many integers $a, b, n$ with $a, b \ge \varepsilon n$ such that $a!\cdot b!$ divides $n!\cdot(a+b-n)!$ while $a+b$ exceeds $n$ by more than $C\cdot\log n$.

Exact FrontierDelta

Prior state unknownproved

Scope and record

Occurred: Jan 6, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-verified. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Erdős Problem #728: Factorial Divisibility · Erdős #728 (Factorials) · Problem 728

Confidence: Not scored

Registry verification: lean verified · announcement · resolved

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Attribution

VibeMathed
registry · event recorded by

Liam Price
human · human collaborator

Kevin Barreto
human · human collaborator

Boris Alexeev
human · human collaborator

Nat Sothanaphan
human · human collaborator

Aristotle (Harmonic) + GPT-5.2 Pro
model · ai model contributor · Harmonic / OpenAI

Lineage and corrections

This event attributed to Boris Alexeev

This event attributed to Kevin Barreto

This event attributed to Liam Price

This event attributed to Nat Sothanaphan

This event attributed to Aristotle (Harmonic) + GPT-5.2 Pro

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