{"paper":{"title":"A certain reciprocal power sum is never an integer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Junyong Zhao, Shaofang Hong, Xiao Jiang","submitted_at":"2018-12-20T17:11:47Z","abstract_excerpt":"By $(\\mathbb{Z}^+)^{\\infty}$ we denote the set of all the infinite sequences $\\mathcal{S}=\\{s_i\\}_{i=1}^{\\infty}$ of positive integers (note that all the $s_i$ are not necessarily distinct and not necessarily monotonic). Let $f(x)$ be a polynomial of nonnegative integer coefficients. Let $\\mathcal{S}_n:=\\{s_1, ..., s_n\\}$ and $H_f(\\mathcal{S}_n):=\\sum_{k=1}^{n}\\frac{1}{f(k)^{s_{k}}}$. When $f(x)$ is linear, Feng, Hong, Jiang and Yin proved in [A generalization of a theorem of Nagell, Acta Math. Hungari, in press] that for any infinite sequence $\\mathcal{S}$ of positive integers, $H_f(\\mathcal{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08705","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":""},"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"}