{"paper":{"title":"A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lihua You, Pingzhi Yuan, Yafei Chen","submitted_at":"2016-06-16T03:38:52Z","abstract_excerpt":"In this paper, we mainly discuss the characterization of a class of arithmetic functions $f: N \\rightarrow C$ such that $f(u^{2}+kv^2)=f^{2}(u)+kf^{2}(v)$ $(k, u, v \\in N)$. We obtain a characterization with given condition, propose a conjecture and show the result holds for $k \\in \\{2, 3, 4, 5 \\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05039","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"}