{"paper":{"title":"Proof of some conjectural hypergeometric supercongruences via curious identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Chen Wang, Zhi-Wei Sun","submitted_at":"2020-06-04T15:01:22Z","abstract_excerpt":"In this paper, we prove several supercongruences conjectured by Z.-W. Sun ten years ago via certain strange hypergeometric identities. For example, for any prime $p>3$, we show that $$\\sum_{k=0}^{p-1}\\frac{\\binom{4k}{2k+1}\\binom{2k}k}{48^k}\\equiv0\\pmod{p^2},$$ and $$ \\sum_{k=0}^{p-1}\\frac{\\binom{2k}{k}\\binom{3k}{k}}{24^k}\\equiv\\begin{cases}\\binom{(2p-2)/3}{(p-1)/3}\\pmod{p^2}\\ &\\mbox{if}\\ p\\equiv1\\pmod{3},\\\\ p/\\binom{(2p+2)/3}{(p+1)/3}\\pmod{p^2}\\ &\\mbox{if}\\ p\\equiv2\\pmod{3}.\\end{cases} $$ We also obtain some other results of such types."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.02918","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.02918/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}