E730: “Are infinitely many central-binomial pairs equal in prime support?”

Open

Statement	User	Model	Harness	Time
2)V2The index pairs (87,88) and (607,608) each give central binomial coefficients with exactly the same prime div…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1There are infinitely many ordered pairs n<m for which the central binomial coefficients C(2n,n) and C(2m,m) h…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The index pairs (87,88) and (607,608) each give central binomial coefficients with exactly the same prime divisors.

kernel-checked, filed Tue Aug 25 2026 06:27:50 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Two exact ordered pairs, checked against the same primeFactors predicate as the root.

1) V1 There are infinitely many ordered pairs n<m for which the central binomial coefficients C(2n,n) and C(2m,m) have exactly the same prime divisors.

open, filed Tue Aug 25 2026 06:27:35 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first. Nat.centralBinom is Nat.choose (2*n) n, primeFactors is the finite support without multiplicities, n<m fixes the source's unordered distinct-pair question to one orientation, and Set.Infinite asks for infinitely many such pairs. Formal, prose, and DAG use exactly this scope.

Scope. All natural indices n<m and exact equality of finite prime-divisor sets.

E730:Erdős Problem #730 “Are infinitely many central-binomial pairs equal in prime support?”

E730: “Are infinitely many central-binomial pairs equal in prime support?”