{"paper":{"title":"A lower bound of Ruzsa's number related to the Erd\\H{o}s-Tur\\'an conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Csaba S\\'andor, Quan-Hui Yang","submitted_at":"2016-12-27T20:06:13Z","abstract_excerpt":"For a set $A\\subseteq \\mathbb{N}$ and $n\\in \\mathbb{N}$, let $R_A(n)$ denote the number of ordered pairs $(a,a')\\in A\\times A$ such that $a+a'=n$. The celebrated Erd\\H{o}s-Tur\\'{a}n conjecture says that, if $R_A(n)\\ge 1$ for all sufficiently large integers $n$, then the representation function $R_A(n)$ cannot be bounded. For any positive integer $m$, Ruzsa's number $R_m$ is defined to be the least positive integer $r$ such that there exists a set $A\\subseteq \\mathbb{Z}_m$ with $1\\le R_A(n)\\le r$ for all $n\\in \\mathbb{Z}_m$. In 2008, Chen proved that $R_{m}\\le 288$ for all positive integers $m$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08722","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"}