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Claim. For a finite set $A$ of positive integers with pairwise distinct subset sums and every real $s>0$,

$$\sum_{n\in A}\frac{1}{n^s}<\frac{1}{1-2^{-s}};$$

at $s=1$ the right side is $2$, which is the statement of Problem 350, so the note settles the problem by a second route. The powers of two show that the constant is sharp for every $s$, since $\sum_{i\ge0}2^{-is}=1/(1-2^{-s})$. The statement is quoted on the problem page from the 1980 monograph of Erdős and Graham (p. 60), which writes "for all real $s\ge0$", and from the site's commentary; at $s=0$ the right side is infinite and the inequality empty, which is why the formal-conjectures variant erdos_350.variants.strengthening takes $s>0$. The Crossref record's deposited abstract says that such a set has a precisely bounded Dirichlet series. The library holds no copy of the note, and no page of this wiki records its argument.

Depends on. Nothing in this wiki.

Acceptance. Refereed publication: Proceedings of the American Mathematical Society 66 (1977), no. 1, 179--180, issued September 1977 (Crossref record, 2026-10-07; the date of this page). Reviewed: the site's curator (T. F. Bloom) records the stronger statement as proved by Hanson, Steele and Stenger in the problem page's commentary, and Erdős and Graham report it as a recent strengthening of Ryavec's theorem in the 1980 monograph (p. 60). The acceptance rests on the publication record and these two reports, not on the note itself. The problem's status-defining source is Ryavec's proof on the Benkoski--Erdős page; this page records the second, stronger route.