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Claim. The answer to Problem 763 is no: for no $A\subseteq\mathbb N$ and no constant $c>0$ is $\sum_{n\le N}1_A*1_A(n)=cN+O(1)$. The claimed result is the theorem of H. L. Montgomery and R. C. Vaughan, On the Erdős–Fuchs theorems, in the form the site's commentary records: for $c>0$ the summatory representation count $\sum_{n\le N}1_A*1_A(n)$ cannot equal $cN+o(N^{1/4})$. This sharpens Theorem 1 of Erdős and Fuchs (their claim page) from the error term $o(N^{1/4}(\log N)^{-1/2})$ to $o(N^{1/4})$; the site credits the improvement to Jurkat, in unpublished work, and to Montgomery and Vaughan. A bounded error term is in particular $o(N^{1/4})$, so the theorem answers the question on its own. The library holds no copy; the statement follows the site's commentary and the formal-conjectures variant erdos_763.variants.montgomery_vaughan, which states it without proof.

Depends on. Nothing in this wiki.

Acceptance. Reviewed: the site's curator, Thomas Bloom, labels the problem DISPROVED and credits the improved error term $o(N^{1/4})$ to Jurkat and to Montgomery and Vaughan in the problem page's commentary (the proof-claim tab is empty and the thread has no posts). The paper appeared in A Tribute to Paul Erdős, Cambridge Univ. Press (1990), 331--338, doi:10.1017/CBO9780511983917.025, an edited volume whose refereeing is not documented, so no refereed evidence is listed; the Crossref record gives only the year, so the page carries the first day of it. The Lean 4 development src/latest/ErdosProblems/Erdos763.lean of Boris Alexeev's lean-proofs repository (first added 2026-08-17; formal authors Codex and GPT-5.6 Sol) names Montgomery and Vaughan, with Erdős and Fuchs, as informal authors of the solution it formalizes, and its not_erdos_763 proves the bounded-error case only, not the $o(N^{1/4})$ error term; the corpus has not built it, so the page lists no formalized evidence.