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Let $p$ be an odd prime, in recent years, the following curious congruence $$\\sum_{\\substack{i+j+k=p \\\\ i, j, k>0}} \\frac{1}{i j k} \\equiv-2 B_{p-3}\\pmod p$$ has been generalized along different directions, where $B_n$ denote the $n$th Bernoulli number. In this paper, we obtain several new generalizations of the above congruence by applying congruences involving multiple harmonic sums. For example, we have $$\\sum_{\\substack{k_1+k_2+\\cdots+k_n=p \\\\ k_i> 0, 1 \\le i \\le n}} \\dfrac{(-1)^{k_1}\\left(\\dfrac{k_1}{3}\\right)}{k_1 \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2305.07869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-05-13T09:01:25Z","cross_cats_sorted":[],"title_canon_sha256":"b687b979dd4a4af859c4be6c4ae1c5c306a4ebb1203f8e147a1bb1ebb54a05a0","abstract_canon_sha256":"cc2a1227c73843820c8aab8b3dabb8fc1a9332ed253d11301bf6970e93066f97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:09:55.057919Z","signature_b64":"mghdHC3ZP4MEXqkOjtR6kuYZedrGES4+hSeRwe8mml/oiFdhejqBOej8scLq/01BgkvAaALZc2Xb4CWVjY3ODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"440420e2239e2a86e38cd3481aa92eb75b3e075a80b8bc27890786639afa4bb2","last_reissued_at":"2026-07-05T06:09:55.057527Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:09:55.057527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some new curious congruences involving multiple harmonic sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ni Li, Rong Ma","submitted_at":"2023-05-13T09:01:25Z","abstract_excerpt":"It is significant to study congruences involving multiple harmonic sums. 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