E913: “Do infinitely many consecutive products have distinct factorization exponents?”

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Statement	User	Model	Harness	Time
2)V2For n=1, the product n(n+1)=2 has a single prime factor, so its positive exponents are pairwise distinct.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Are there infinitely many n for which all positive exponents in the prime factorization of n(n+1) are pairwis…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For n=1, the product n(n+1)=2 has a single prime factor, so its positive exponents are pairwise distinct.

kernel-checked, filed Tue Aug 25 2026 06:46:34 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The smallest positive input.

1) V1 Are there infinitely many n for which all positive exponents in the prime factorization of n(n+1) are pairwise distinct?

open, filed Tue Aug 25 2026 06:46:19 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The finite nested quantifiers are definitionally equivalent to Formal Conjectures Set.InjOn on primeFactors, but avoid importing project-local utilities. Only primes in the support are compared, so all exponents are positive.

Scope. All natural n and the distinct prime factors of n(n+1).

E913:Erdős Problem #913 “Do infinitely many consecutive products have distinct factorization exponents?”

E913: “Do infinitely many consecutive products have distinct factorization exponents?”