{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PXZ5TNWDV2X5JJ5SZ773MVDHTX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a0b7e157eb41fca45c644e11dca7519b2272c2c43389f522e43dc29b6d5db6d2","cross_cats_sorted":["cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-02-08T20:08:08Z","title_canon_sha256":"4e22fbd1e0152af26715fb81302c0f59ac099feb42d125ac328ea84081fe7896"},"schema_version":"1.0","source":{"id":"1002.1679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1679","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1679v2","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1679","created_at":"2026-05-18T04:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"PXZ5TNWDV2X5","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PXZ5TNWDV2X5JJ5S","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PXZ5TNWD","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:7ea4580628a158c13e47e6700c0a7e6c3c6c786c967f97d7afd3ba2f02b09008","target":"graph","created_at":"2026-05-18T04:20:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We describe how to compute the intersection of two Lucas sequences of the forms $\\{U_n(P,\\pm 1) \\}_{n=0}^{\\infty}$ or $\\{V_n(P,\\pm 1) \\}_{n=0}^{\\infty}$ with $P\\in\\mathbb{Z}$ that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case $U_n(1,-1)$ and $U_n(3,1)$ and the case of two $V$-sequences when the product of their discriminants is a perfect square. Moreover, the intersection in these cases also forms a Lucas sequence. Our approach relies on solving homogeneous quadratic Diophantine equations and Thue equation","authors_text":"Max A. Alekseyev","cross_cats":["cs.DM","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-02-08T20:08:08Z","title":"On the intersections of Fibonacci, Pell, and Lucas numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1679","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8b527265d78b1417100b38403259062e0af02f8baf83b456c7ad2ce8f36d5975","target":"record","created_at":"2026-05-18T04:20:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a0b7e157eb41fca45c644e11dca7519b2272c2c43389f522e43dc29b6d5db6d2","cross_cats_sorted":["cs.DM","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-02-08T20:08:08Z","title_canon_sha256":"4e22fbd1e0152af26715fb81302c0f59ac099feb42d125ac328ea84081fe7896"},"schema_version":"1.0","source":{"id":"1002.1679","kind":"arxiv","version":2}},"canonical_sha256":"7df3d9b6c3aeafd4a7b2cfffb654679df14fd222d505c6d5cf2a5d204244de7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7df3d9b6c3aeafd4a7b2cfffb654679df14fd222d505c6d5cf2a5d204244de7c","first_computed_at":"2026-05-18T04:20:13.233800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:13.233800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RPKlGvDxPxbzMCMLImHt9LDT0tbgoNiABatbN0XBCj5aVR56KWq57YcS3Jv5bD3feowPs5VUuHQBUva3BGLMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:13.234246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b527265d78b1417100b38403259062e0af02f8baf83b456c7ad2ce8f36d5975","sha256:7ea4580628a158c13e47e6700c0a7e6c3c6c786c967f97d7afd3ba2f02b09008"],"state_sha256":"64c12dfa3cc8c625931a54c10757ab915fb331c4b2c8621669bb25f2dd0518be"}