{"paper":{"title":"Proof of Sun's conjecture on the divisibility of certain binomial sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Victor J. W. Guo","submitted_at":"2013-01-21T14:39:37Z","abstract_excerpt":"In this paper, we prove the following result conjectured by Z.-W. Sun: $$ (2n-1){3n\\choose n}| \\sum_{k=0}^{n}{6k\\choose 3k}{3k\\choose k}{6(n-k)\\choose 3(n-k)}{3(n-k)\\choose n-k}. $$ by showing that the left-hand side divides each summand on the right-hand side."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4877","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"}