{"paper":{"title":"A Geometric Consideration of the Erd\\H{o}s-Straus Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eugen Ionascu, Kyle Bradford","submitted_at":"2014-11-13T00:30:49Z","abstract_excerpt":"In this paper we will explore the solutions to the diophantine equation in the Erd\\H{o}s-Straus conjecture. For a prime $p$ we are discussing the relationship between the values $x,y,z \\in \\mathbb{N}$ so that $$ \\frac{4}{p} = \\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}.$$\n  We will separate the types of solutions into two cases. In particular we will argue that the most common relationship found is $$ x = \\lfloor \\frac{py}{4y-p} \\rfloor + 1.$$\n  Finally, we will make a few conjectures to motivate further research in this area."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3403","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"}