{"paper":{"title":"Three consecutive almost squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jeremy Rouse, Yilin Yang","submitted_at":"2015-02-02T20:15:37Z","abstract_excerpt":"Given a positive integer $n$, we let ${\\rm sfp}(n)$ denote the squarefree part of $n$. We determine all positive integers $n$ for which $\\max \\{ {\\rm sfp}(n), {\\rm sfp}(n+1), {\\rm sfp}(n+2) \\} \\leq 150$ by relating the problem to finding integral points on elliptic curves. We also prove that there are infinitely many $n$ for which \\[\n  \\max \\{ {\\rm sfp}(n), {\\rm sfp}(n+1), {\\rm sfp}(n+2) \\} < n^{1/3}. \\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00605","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"}