{"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. 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 \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.07869","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.07869/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"}