{"paper":{"title":"On Erd\\H{o}s and S\\'ark\\\"ozy's sequences with Property P","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christian Elsholtz, Stefan Planitzer","submitted_at":"2016-09-26T11:51:16Z","abstract_excerpt":"A sequence $A$ of positive integers having the property that no element $a_i \\in A$ divides the sum $a_j+a_k$ of two larger elements is said to have `Property P'. We construct an infinite set $S\\subset \\mathbb{N}$ having Property P with counting function $S(x)\\gg\\frac{\\sqrt{x}}{\\sqrt{\\log x}(\\log\\log x)^2(\\log \\log \\log x)^2}$. This improves on an example given by Erd\\H{o}s and S\\'ark\\\"ozy with a lower bound on the counting function of order $\\frac{\\sqrt{x}}{\\log x}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07935","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"}