{"paper":{"title":"A question of S\\'{a}rkozy and S\\'{o}s on representation functions] {A question of S\\'{a}rkozy and S\\'{o}s on representation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.CV"],"primary_cat":"math.NT","authors_text":"Lianrong Ma, Yan Li","submitted_at":"2011-08-09T13:14:53Z","abstract_excerpt":"For $m\\geq 1$, let $0<b_0<b_1<...<b_m$ and $\\ e_0,e_1,...,e_m>0$ be fixed positive integers. Assume there exists a prime $p$ and an integer $t>0$ such that $p^t\\mid b_0$, but $p^t\\nmid b_{i}\\ {\\rm for}\\ 1\\leq i\\leq m$.\n  Then, we prove that there is no infinite subset $\\mathcal A$ of positive integers, such that the number of solutions of the following equation $$n=b_0(a_{0,1}+...+a_{0,e_0})+...+b_m(a_{m,1}+...+a_{m,r_m}),\\ a_{i,j}\\in \\mathcal A$$ is constant for $n$ large enough. This result generalizes the recent result of Cilleruelo and Ru\\'{e} for bilinear case, and answers a question pose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1920","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"}