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Suppose that $b\\neq 0$ and $(a,b)\\neq (2,-1), (-2, -1)$. Then there exist two relatively prime positive integers $x_0$, $x_1$ such that $|x_n|$ is a composite integer for all $n\\in \\mathbb{N}$.\n  The above theorem extends a result of Graham who solved the problem when $(a,","authors_text":"Adrienne Ko, Celine Lee, Dan Ismailescu, Jae Yong Park","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-19T15:57:58Z","title":"On second order linear sequences of composite numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08041","kind":"arxiv","version":1},"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":"sha256:4ff8e8b9d3e65c4511463303e0449e041cd8ba673c830d6f8b07fb4ccc860507","target":"record","created_at":"2026-05-17T23:57:55Z","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":"d0d19828f1416c9585aa55eb74ce89fc0e6eb29f4d7e2f684394c2af35b57c3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-19T15:57:58Z","title_canon_sha256":"1b357d8ae15a61f6a5d8b56ec0442e9d582788163ebb779ad71ffeb4aabd89c3"},"schema_version":"1.0","source":{"id":"1812.08041","kind":"arxiv","version":1}},"canonical_sha256":"4b755f7b9e4a93a4f25021ca01e2bbc7270aefc7961a4a8891032fd78831837a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b755f7b9e4a93a4f25021ca01e2bbc7270aefc7961a4a8891032fd78831837a","first_computed_at":"2026-05-17T23:57:55.083103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:55.083103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sgv7po8u6fxmbi8YBEOqLIHAAxks0BTEZiOYWnd+sQV0dV5e8ViJ9AKiYddmKGosQEPwAfDMvz+5Qrut/II3AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:55.083749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.08041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ff8e8b9d3e65c4511463303e0449e041cd8ba673c830d6f8b07fb4ccc860507","sha256:43ef2a12dd20c67ae8dc0731b03e3d7361d0dbe751687c5b2ea843b226c98ea4"],"state_sha256":"fd836efe1024b87bb47da930d97bd922b27f1f32b38f869210c72e39c5cfb1ad"}