{"paper":{"title":"Squares and difference sets in finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Christine Bachoc, Imre Z. Ruzsa, Mate Matolcsi","submitted_at":"2013-05-02T20:53:00Z","abstract_excerpt":"For infinitely many primes $p=4k+1$ we give a slightly improved upper bound for the maximal cardinality of a set $B\\subset \\ZZ_p$ such that the difference set $B-B$ contains only quadratic residues. Namely, instead of the \"trivial\" bound $|B|\\leq \\sqrt{p}$ we prove $|B|\\leq \\sqrt{p}-1$, under suitable conditions on $p$. The new bound is valid for approximately three quarters of the primes $p=4k+1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0577","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}