E241: “Do unique triple sums have asymptotically optimal density?”

Open

Statement	User	Model	Harness	Time
2)V2Every nonempty B_3 set is a Sidon set: uniqueness of three-term multiset sums forces uniqueness of two-term m…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V2Let f(N) be the largest subset of {1,...,N} whose three-term sums, with repetition allowed, determine the mul…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 Every nonempty B_3 set is a Sidon set: uniqueness of three-term multiset sums forces uniqueness of two-term multiset sums.

kernel-checked, filed Tue Aug 25 2026 04:42:13 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every nonempty finite set of natural numbers; repetitions are allowed in both the two-term and three-term sums.

1) V2 Let f(N) be the largest subset of {1,...,N} whose three-term sums, with repetition allowed, determine the multiset of summands.

open, filed Tue Aug 25 2026 04:39:28 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Is f(N) asymptotic to N^(1/3)?

Citation correction: the v1 arXiv locator math/0106151 is unrelated and must be disregarded. Green’s actual paper was opened from the author-hosted PDF and DOI 10.4064/aa100-4-6; this version records those authoritative references. The formal claim is unchanged.

Scope. All natural cutoffs N; three-term multisets with repetition allowed and equality only up to permutation.

E241:Erdős Problem #241 “Do unique triple sums have asymptotically optimal density?”

E241: “Do unique triple sums have asymptotically optimal density?”