{"paper":{"title":"Proof of a congruence concerning truncated hypergeometric series ${}_6F_5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Chen Wang","submitted_at":"2018-12-26T15:22:31Z","abstract_excerpt":"In this paper, we mainly prove the following congruence conjectured by J.-C. Liu: $$ {}_6F_5\\bigg[\\begin{matrix}\\frac{5}{4}&\\frac{1}{2}&\\frac{1}{2}&\\frac{1}{2}&\\frac{1}{2}&\\frac{1}{2}\\\\&\\frac{1}{4}&1&1&1&1\\end{matrix}\\bigg|\\ -1\\bigg]_{\\frac{p-1}{2}}\\equiv-\\frac{p^3}{16}\\Gamma_p\\left(\\frac{1}{4}\\right)^4\\pmod{p^5}, $$ where $p\\geq5$ are primes with $p\\equiv3\\pmod{4}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10324","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"}