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The claim. Theorem 1 of J. E. Olson, An addition theorem modulo $p$, J. Combinatorial Theory 5 (1968), no. 1, 45--52, p. 45: if $a_1,\ldots,a_s$ are distinct nonzero residue classes modulo a prime $p$ and $s>(4p-3)^{1/2}$, then every residue class, $0$ included, is a sum $\epsilon_1a_1+\cdots+\epsilon_sa_s$ with each $\epsilon_i$ equal to $0$ or $1$ and not all $0$. Paged as Theorem 1 of Olson (1968). A set $A\subseteq\mathbb Z/p\mathbb Z$ with $|A|\ge2\sqrt p$ either contains $0$ or consists of more than $(4p-3)^{1/2}$ nonzero residues, and in both cases has a nonempty zero-sum subset; the statement of Problem 540 thus holds for prime $N$ with the constant $2$, Erdős and Heilbronn's conjectured constant. The paper prints no received date, so the page is named by the issue, July 1968 according to its Crossref record, with the first day of the month standing in for the unknown day.

Covers. The problem for prime $N$: more than $(4p-3)^{1/2}$ distinct nonzero residues modulo $p$ have a nonempty zero-sum subfamily. Composite $N$ is not covered.

Acceptance. Refereed: the journal publication. Reviewed: the site's curator, Thomas Bloom, who is independent of the author, labels the problem PROVED (LEAN) and his commentary credits the prime case to this paper; Szemerédi's 1970 paper records in an editor's footnote that Olson proved the prime case.

Depends on. No page of this wiki.