{"paper":{"title":"Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Jiang Zeng, Victor J. W. Guo","submitted_at":"2011-01-05T14:14:32Z","abstract_excerpt":"The Apery polynomials are defined by $A_n(x)=\\sum_{k=0}^{n}{n\\choose k}^2{n+k\\choose k}^2 x^k$ for all nonnegative integers $n$. We confirm several conjectures of Z.-W. Sun on the congruences for the sum $\\sum_{k=0}^{n-1}(-1)^k(2k+1) A_k(x)$ with $x\\in Z$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0983","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"}