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In this paper we prove the existence of an infinite family of hyperelliptic curves on which there is a sequence of rational points in a geometric progression of length at least eight."},"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":"1602.05850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-18T16:03:37Z","cross_cats_sorted":[],"title_canon_sha256":"b670c77472fc83c705a3f78d0a632ad3497a4a0fceb4f9d36287d4b4521d111b","abstract_canon_sha256":"436dad1c04ef7d1014960d11f1d450a89307f8161431ecf2b20bc4c4d5777756"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:41.106520Z","signature_b64":"1GaURjUR/VoH3mcdkSWTFUQLsQ8Q+W+Gmq7pzw/fJ3jZebruCWVaVnpMrphqPup9Yq/D87CTgrPtoIqpfo8BCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23dd11f188f287c0e2f3412d9abec6fd0220c843763fe6b2c707fcd6cf70fe43","last_reissued_at":"2026-05-18T01:11:41.106092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:41.106092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On geometric progressions on hyperelliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mohamed Alaa, Mohammad Sadek","submitted_at":"2016-02-18T16:03:37Z","abstract_excerpt":"Let $C$ be a hyperelliptic curve over $\\mathbb Q$ described by $y^2=a_0x^n+a_1x^{n-1}+\\ldots+a_n$, $a_i\\in\\mathbb Q$. 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