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In a recent paper, Amdeberhan, Chen, Moll, and Sagan considered some arithmetic properites of the generalized Fibonacci sequence. Specifically, they considered the behavior of analogues of the $p$-adic valuation and the Riemann zeta function. In this paper, we resolve some conjectures which they raised relating to these topics. We also consider the rank modulo $n$ in more d"},"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":"1407.8086","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2014-07-30T15:22:52Z","cross_cats_sorted":[],"title_canon_sha256":"d35b032d7579978bdbe86538d2fbf270fc29c081e59020383a86d30a867693b7","abstract_canon_sha256":"3ffdbe8e4e662123a5813506143f4bf16bf286116a7c9d6c3512ba17aa712ca5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:13.637499Z","signature_b64":"sRTry+E+bfxHciCM4KOcHGhngcqPO+dFKFpFJZloTLGgtLSs3XIBGgsLP7fr3fOKa4HnsOhzJh1eDrZhMayCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ecd695694a4a89721cda73acc53bf7adea1439ad9d0b98365af011f18f19a50","last_reissued_at":"2026-05-18T02:46:13.636748Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:13.636748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetic properties of generalized Fibonacci sequences","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Soohyun Park","submitted_at":"2014-07-30T15:22:52Z","abstract_excerpt":"The generalized Fibonacci sequences are sequences $\\{f_n\\}$ which satisfy the recurrence $f_n(s, t) = sf_{n - 1}(s, t) + tf_{n - 2}(s, t)$ ($s, t \\in \\mathbb{Z}$) with initial conditions $f_0(s, t) = 0$ and $f_1(s, t) = 1$. In a recent paper, Amdeberhan, Chen, Moll, and Sagan considered some arithmetic properites of the generalized Fibonacci sequence. Specifically, they considered the behavior of analogues of the $p$-adic valuation and the Riemann zeta function. In this paper, we resolve some conjectures which they raised relating to these topics. 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