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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 $r\\ge 5$."},"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":"1602.05862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-18T16:28:16Z","cross_cats_sorted":[],"title_canon_sha256":"abda26aa0100c631e7b861f85bf7d47157547e624d06340e1f7689cf397953c9","abstract_canon_sha256":"d230350fe5946d274105f3627fd375503559174baa697c33b9d9aeb77a711096"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:11.619163Z","signature_b64":"n/mnhnfG3GIjVHWJQT+c6Qxn4rusJg2OPZFXqZQX4Kymi5FAy0ptPVBtg57d0EiPt6h+CJxxhEXKeEX6T9VVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ebd2363abe7e725e07a722f8de9c1d175eea2b55babb516e39ce25b9adbd755","last_reissued_at":"2026-05-18T00:38:11.618495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:11.618495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $C(\\mathbb Q)$. 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