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
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
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