{"paper":{"title":"How to prove this polynomial always has integer values at all integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Wilberd van der Kallen","submitted_at":"2015-09-29T15:40:33Z","abstract_excerpt":"The following problem was posed by user \"Kevin\" on Mathoverflow. How to prove this polynomial always has integer values at all integers? $$P_m(x)=\\sum_{i=0}^{m}\\sum_{j=0}^{m} \\binom{x+j}{j} \\binom{x-1}{j} \\binom{j}{i} \\binom{m}{i} \\binom{i}{m-j} \\frac{3}{(2i-1)(2j+1)(2m-2i-1)}.$$\n  We provide an answer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08811","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"}