{"paper":{"title":"Ternary Egyptian fractions with prime denominator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Adva Mond, Julien Portier","submitted_at":"2022-01-27T20:51:29Z","abstract_excerpt":"For a prime number $p$, let $A_3(p)= | \\{ m \\in \\mathbb{N}: \\exists m_1,m_2,m_3 \\in \\mathbb{N}, \\frac{m}{p}=\\frac{1}{m_1}+\\frac{1}{m_2}+\\frac{1}{m_3} \\} |$. In 2019 Luca and Pappalardi proved that $x (\\log x)^3 \\ll \\sum_{p \\le x} A_{3}(p) \\ll x (\\log x)^5$. We improve the upper bound, showing $\\sum_{p \\le x} A_{3}(p) \\ll x (\\log x)^3 (\\log \\log x)^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.11805","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.11805/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}