{"paper":{"title":"Exact additive complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Imre Z. Ruzsa","submitted_at":"2015-10-03T12:59:25Z","abstract_excerpt":"Let $A,B$ be sets of positive integers such that $A+B$ contains all but finitely many positive integers. S\\'ark\\\"ozy and Szemer\\'edi proved that if $ A(x)B(x)/x \\to 1$, then $A(x)B(x)-x \\to \\infty $. Chen and Fang considerably improved S\\'ark\\\"ozy and Szemer\\'edi's bound. We further improve their estimate and show by an example that our result is nearly best possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00812","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"}