{"paper":{"title":"On sequences of consecutive squares on elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mohamed Kamel, Mohammad Sadek","submitted_at":"2016-02-18T16:28:16Z","abstract_excerpt":"Let $C$ be an elliptic curve defined over $\\mathbb Q$ by the equation $y^2=x^3+Ax+B$ where $A,B\\in\\mathbb Q$. A sequence of rational points $(x_i,y_i)\\in C(\\mathbb Q),\\,i=1,2,\\ldots,$ is said to form a sequence of consecutive squares on $C$ if the sequence of $x$-coordinates, $x_i,i=1,2,\\ldots$, consists of consecutive squares. We produce an infinite family of elliptic curves $C$ with a $5$-term sequence of consecutive squares. Furthermore, this sequence consists of five independent rational points in $C(\\mathbb Q)$. In particular, the rank $r$ of $C(\\mathbb Q)$ satisfies $r\\ge 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05862","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"}