{"paper":{"title":"Higher-Order Congruence for Reciprocal Power Sums and Generalized Lehmer-Type Products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hao Zhong, Zhenming Tang","submitted_at":"2026-07-13T05:43:03Z","abstract_excerpt":"This paper investigates high-order congruences of reciprocal power sums and Lehmer-type products. Let $n\\geq 1$ with $(n,6)=1$ and $e\\in\\{2,3,4,6\\}$. For the reciprocal square sums \\begin{equation*}\n  S(n)=\\sum_{\\substack{r=1 \\\\ (r,n)=1}}^{\\lfloor n/e \\rfloor}\\frac{1}{r^2} \\end{equation*} we already know the form of the congruence modulo $n$. In this paper, motivated by the known congruences, we first extend these results to certain reciprocal sums of odd order and establish a uniform congruence modulo $n$ for \\begin{equation*}\n  S_m(n)=\\sum_{\\substack{r=1 \\\\ (r,n)=1}}^{\\lfloor n/e \\rfloor}\\fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11113","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/2607.11113/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"}