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For any $p$-adic integer $a$, we determine $$\\sum_{k=0}^{p-1}\\binom{-a}k\\binom{a-1}kH_k,\\ \\ \\sum_{k=0}^{p-1}\\binom{-a}k\\binom{a-1}kH_k^{(2)},\\ \\ \\sum_{k=0}^{p-1}\\binom{-a}k\\binom{a-1}k\\frac{H_k^{(2)}}{2k+1}$$ modulo $p^2$, where $H_k=\\sum_{0<j\\le k}1/j$ and $H_k^{(2)}=\\sum_{0<j\\le k}1/j^2$. In particular, we show that \\begin{gather*}\\sum_{k=0}^{p-1}\\binom{-a}k\\binom{a-1}kH_k\\equiv(-1)^{\\langle a\\rangle_p}\\,2\\left(B_{p-1}(a)-B_{p-1}\\right)\\pmod p, \\\\\\sum_{k=0}^{p-1}\\binom{-a}k\\binom{a-1}kH_k^{(2)}\\equiv -E_{p-3}(a)\\pmod p, \\\\(2a-1)\\sum_{k=0}^{p-1}\\binom{-a}k\\binom{a-1}k\\fr","authors_text":"Zhi-Wei Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-31T15:53:32Z","title":"New congruences involving harmonic numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8465","kind":"arxiv","version":5},"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":"sha256:0a27c5b162e826790fb0ca73d58fc9e8dd90c45708857322f80e6cf2f8d1b100","target":"record","created_at":"2026-07-05T07:31:49Z","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":"398a2aba4cc3dd76c8e5eb7c09780192aaec2322be8a4a2999f9bd8a74909c46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-07-31T15:53:32Z","title_canon_sha256":"09589902e164767c41a4558d2917079b1d8838421c384c06e2e6fb8a97de5498"},"schema_version":"1.0","source":{"id":"1407.8465","kind":"arxiv","version":5}},"canonical_sha256":"3db5f84b1e51aecf1a03e5b9f95b63e166ebffed01d3c9964907bb1a9f2fecff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3db5f84b1e51aecf1a03e5b9f95b63e166ebffed01d3c9964907bb1a9f2fecff","first_computed_at":"2026-07-05T07:31:49.741043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:31:49.741043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YlkG4sosnyQKSqAZ+KPcO5Iruii5SWugxXGKI67cSXHIiS4vIAP7KoRLv2jJg4jGzXjt8DcAfi0us6Z7WXCcDg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:31:49.741580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.8465","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a27c5b162e826790fb0ca73d58fc9e8dd90c45708857322f80e6cf2f8d1b100","sha256:0cd9dedcfb178af930da5c46bfacc06cb9c21149f607316138661ca41e2d53b5"],"state_sha256":"2b5a41d6343d4ecaefa696c7b52a36eaac5092ab1be2073acd5941935e7b0550"}