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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 $5$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.01158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-04T15:17:51Z","cross_cats_sorted":[],"title_canon_sha256":"56b6c388d469370131f5a80754eac2afd32655969113f6bdac734c67ea63d364","abstract_canon_sha256":"602438873e949836e85146cf00a5e48a92131764fe41e4f88662dd337f41dea3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:17.283492Z","signature_b64":"1oqM3YrVlC3X+wBNS1A9L7bLYMEhMrvUqos2yBHYgDjGnbvtpVtXb1czze+gyi8sa5z6N5SzJYu43BQXtlByBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4697f709f71e4f848aea641c0d96b2fbc030138d495ee06e4318fdbdd3c4fb2f","last_reissued_at":"2026-05-18T00:14:17.282764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:17.282764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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