{"paper":{"title":"On Menon-Sury's identity with several Dirichlet characters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Man Chen, Su Hu, Yan Li","submitted_at":"2018-07-19T05:26:19Z","abstract_excerpt":"The Menon-Sury's identity is as follows: \\begin{equation*} \\sum_{\\substack{1 \\leq a, b_1, b_2, \\ldots, b_r \\leq n\\\\\\mathrm{gcd}(a,n)=1}} \\mathrm{gcd}(a-1,b_1, b_2, \\ldots, b_r,n)=\\varphi(n) \\sigma_r(n), \\end{equation*} where $\\varphi$ is Euler's totient function and $\\sigma_r(n)=\\sum_{d\\mid n}{d^r}$. Recently, Li, Hu and Kim \\cite{L-K} extended the above identity to a multi-variable case with a Dirichlet character, that is, they proved\n  \\begin{equation*} \\sum_{\\substack{a\\in\\Bbb Z_n^\\ast \\\\ b_1, \\ldots, b_r\\in\\Bbb Z_n}} \\mathrm{gcd}(a-1,b_1, b_2, \\ldots, b_r,n)\\chi(a)=\\varphi(n)\\sigma_r{\\left"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07241","kind":"arxiv","version":2},"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"}