{"paper":{"title":"On divisibility of sums of Apery polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Hao Pan","submitted_at":"2011-08-07T14:57:51Z","abstract_excerpt":"For any positive integers $m$ and $\\alpha$, we prove that $$\\sum_{k=0}^{n-1}\\epsilon^k(2k+1)A_k^{(\\alpha)}(x)^m\\equiv0\\pmod{n}, $$ where $\\epsilon\\in\\{1,-1\\}$ and $$ A_n^{(\\alpha)}(x)=\\sum_{k=0}^n\\binom{n}{k}^{\\alpha}\\binom{n+k}{k}^{\\alpha}x^k.$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1546","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"}