{"paper":{"title":"Elliptic Curves Containing Sequences of Consecutive Cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gamze Sava\\c{s} \\c{C}elik, G\\\"okhan Soydan","submitted_at":"2018-06-04T15:17:51Z","abstract_excerpt":"Let $E$ be an elliptic curve over $\\mathbb{Q}$ described by $y^2= x^3+ Kx+ L$ where $K, L \\in \\mathbb{Q}$. A set of rational points $(x_i,y_i) \\in E(\\mathbb{Q})$ for $i=1, 2, \\cdots, k$, is said to be a sequence of consecutive cubes on $E$ if the $x-$coordinates of the points $x_i$'s for $i=1, 2, \\cdots$ form consecutive cubes. In this note, we show the existence of an infinite family of elliptic curves containing a length-$5$-term sequence of consecutive cubes. Morever, these five rational points in $E (\\mathbb{Q})$ are linearly independent and the rank $r$ of $E(\\mathbb{Q})$ is at least $5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01158","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"}