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By applying Matveev's theorem, which provides lower bounds for linear forms in logarithms of algebraic numbers, along with a modified Baker-Davenport reduction method and a divisibility property of Fibonacci numbers, we show that $(n, l, k, m) = (6, 3, 3, 1)$ is the only positive integer quadr"},"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":"2409.02047","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-09-03T16:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"c3664846e1e93dc958a1ed64a94b9abe4f68fc6f5fc3c3b60ca055e0700728d2","abstract_canon_sha256":"fd4e7112fe0ef31d869acf20f14af471b98f465dc6f6970a17c056d085e9aac5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:50:05.048617Z","signature_b64":"i8af/0KbX3OJz272tbiQTwnGygtny0jiWvgcRWQznDQHsFhWjVCkXtdUGcSn94CumwcOPu//4JunxYqkTC6+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea3ea7d3be24d2236d283c4f1b7f78ebd2ffcd0a05e0f90148e0dbe6b5baee55","last_reissued_at":"2026-07-05T09:50:05.047944Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:50:05.047944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Diophantine Equation $F_n = F_l^k (F_l^m-1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nazim I. 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