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We show that the integer sequence $(z_n)$ defined by $nP=(x_n/z_n^2,y_n/z_n^3)$ for all $n\\ge 1$ does not eventually coincide with $(u_{n^2})$ for any choice of linear recurrence sequence $(u_n)$ with integer values."},"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":"1610.08109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-25T22:06:01Z","cross_cats_sorted":[],"title_canon_sha256":"52201bf9aee3a63c05095a253a470a7bcb2e9a755dfc584185189ae53f88170f","abstract_canon_sha256":"96f2ca73cdae27e2799aeac59425e807a63e05c3d7a30b2aa34fe8a2b366bcf8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:45.266553Z","signature_b64":"94p+G0/xcWoaurqVagxLyuyssOCcA5horLNNrbm1dQ9vs3nu23gvJrdE882t4QIY781UslRmh0u1BpgtszwQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd9e85119c994035df09f768a052df3c823a73d7aaeee8a57b53a876fcc467a5","last_reissued_at":"2026-05-18T00:56:45.265839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:45.265839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An elliptic sequence is not a sampled linear recurrence sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florian Luca, Tom Ward","submitted_at":"2016-10-25T22:06:01Z","abstract_excerpt":"Let $E$ be an elliptic curve defined over the rationals and in minimal Weierstrass form, and let $P=(x_1/z_1^2,y_1/z_1^3)$ be a rational point of infinite order on $E$, where $x_1,y_1,z_1$ are coprime integers. We show that the integer sequence $(z_n)$ defined by $nP=(x_n/z_n^2,y_n/z_n^3)$ for all $n\\ge 1$ does not eventually coincide with $(u_{n^2})$ for any choice of linear recurrence sequence $(u_n)$ with integer values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08109","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.08109","created_at":"2026-05-18T00:56:45.265951+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.08109v1","created_at":"2026-05-18T00:56:45.265951+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08109","created_at":"2026-05-18T00:56:45.265951+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWPIKEM4TFAD","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWPIKEM4TFADLXYJ","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWPIKEM4","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS","json":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS.json","graph_json":"https://pith.science/api/pith-number/XWPIKEM4TFADLXYJ65UKAUW7HS/graph.json","events_json":"https://pith.science/api/pith-number/XWPIKEM4TFADLXYJ65UKAUW7HS/events.json","paper":"https://pith.science/paper/XWPIKEM4"},"agent_actions":{"view_html":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS","download_json":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS.json","view_paper":"https://pith.science/paper/XWPIKEM4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.08109&json=true","fetch_graph":"https://pith.science/api/pith-number/XWPIKEM4TFADLXYJ65UKAUW7HS/graph.json","fetch_events":"https://pith.science/api/pith-number/XWPIKEM4TFADLXYJ65UKAUW7HS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/action/storage_attestation","attest_author":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/action/author_attestation","sign_citation":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/action/citation_signature","submit_replication":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/action/replication_record"}},"created_at":"2026-05-18T00:56:45.265951+00:00","updated_at":"2026-05-18T00:56:45.265951+00:00"}