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We confirm a conjecture of Sun and prove that $${}_{2r+1}F_{2r}\\bigg[\\begin{matrix}\\alpha&\\alpha&\\ldots&\\alpha\\\\ &1&\\ldots&1\\end{matrix}\\bigg|\\,1\\bigg]_{p-1}\\equiv0\\pmod{p^2},$$ where the truncated hypergeometric series $$ {}_{q+1}F_{q}\\bigg[\\begin{matrix}x_0&x_1&\\ldots&x_{q}\\\\ &y_1&\\ldots&y_q\\end{matrix}\\bigg|\\,z\\bigg]_{n}:=\\sum_{k=0}^n\\frac{(x_0)_k(x_1)_k\\cdots(x_q)_k}{(y_1)_k\\cdot (y_q)_k}\\cdot\\frac{z^k}{k!}. $$","authors_text":"Guo-Shuai Mao, Hao Pan","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-07T16:57:43Z","title":"On the divisibility of some truncated hypergeometric series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02213","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:48de45ba2d760fb5147a5573e5c215828a0af4f5773fb4a6da7c6bc68d8dfbed","target":"record","created_at":"2026-05-18T00:22:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3d8caa13fe92aac658fbe263c67506c33578436ab53af963cf39c7601789356a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-07T16:57:43Z","title_canon_sha256":"d33d92f28a75386a7e7dd0486e16f48052e7ebf863ae660381b5f9d2c1f4aab1"},"schema_version":"1.0","source":{"id":"1801.02213","kind":"arxiv","version":2}},"canonical_sha256":"c85f765cb655173384b6ad33a5a681a8334850b35f118df6cde6b4d190890933","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c85f765cb655173384b6ad33a5a681a8334850b35f118df6cde6b4d190890933","first_computed_at":"2026-05-18T00:22:02.389730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:02.389730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hAuWWbmNEwoJIJ9MNz7VAq/d2Nmlr/vPBnJsSLy8Xj+jCVcEI/m8O+BmX0hEb7n2s8POn3XIEwuHDbM30KG4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:02.390326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48de45ba2d760fb5147a5573e5c215828a0af4f5773fb4a6da7c6bc68d8dfbed","sha256:dd4801de7998b3c3d3b7832c7fd30ce1f7766da770fba6df33ddcf093302eb16"],"state_sha256":"8b3e8e952d4156fdfcf598547f3efcaaf2f897009bd1ad327bd152fea42cbef8"}