{"paper":{"title":"Rational Points on Erdos-Selfridge Superelliptic Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Bennett, Samir Siksek","submitted_at":"2015-10-19T08:15:22Z","abstract_excerpt":"Given $k \\geq 2$, we show that there are at most finitely many rational numbers $x$ and $y \\neq 0$ and integers $\\ell \\geq 2$ (with $(k,\\ell) \\neq (2,2)$) for which $$ x (x+1) \\cdots (x+k-1) = y^\\ell. $$ In particular, if we assume that $\\ell$ is prime, then all such triples $(x,y,\\ell)$ satisfy either $y=0$ or $\\log \\ell < 3^k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05376","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"}