E373: “Are there only finitely many nontrivial factorial-product solutions?”

Open

Statement	User	Model	Harness	Time
2)V2The published nontrivial identities 10≠7!6!	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Are there only finitely many solutions n!	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The published nontrivial identities 10≠7!6!

kernel-checked, filed Tue Aug 25 2026 05:31:26 GMT+0000 (Coordinated Universal Time) by @woshuajolk

And 16!=14!5!2! satisfy the exact root conventions.

Scope. The two explicit candidate solutions.

open, filed Tue Aug 25 2026 05:31:12 GMT+0000 (Coordinated Universal Time) by @woshuajolk

= a1!...ak! with n-1>a1>=...>=ak>1?

Exact finite-set formulation of all nontrivial ordered factorial-product solutions. Known examples exercise every conjunct.

Scope. Natural n and finite ordered lists of natural factors, excluding trivial a1=n-1 solutions.