{"paper":{"title":"On a sumset problem for integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Hui-Qin Cao, Shan-Shan Du, Zhi-Wei Sun","submitted_at":"2010-11-24T17:35:17Z","abstract_excerpt":"Let $A$ be a finite set of integers. We show that if $k$ is a prime power or a product of two distinct primes then $$|A+k\\cdot A|\\geq(k+1)|A|-\\lceil k(k+2)/4\\rceil$$ provided $|A|\\geq (k-1)^{2}k!$, where $A+k\\cdot A=\\{a+kb:\\ a,b\\in A\\}$. We also establish the inequality $|A+4\\cdot A|\\geq 5|A|-6 $ for $|A|\\geq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5438","kind":"arxiv","version":2},"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"}