The Order of the Fibonacci and Lucas Numbers

1995/06/01 by T. Lengyel, Tamás Lengyel · 68 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics #Economics #Fibonacci number #Fibonacci polynomials #Lucas number #Lucas sequence #Mathematics #Mathematics and Applications #Order (exchange) #Pisano period

paper · doi:10.1080/00150517.1995.12429139

published in The Fibonacci Quarterly 33(3), 234-239 (The Fibonacci Association)

openalex publication_date 1995/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

In this paper vp(r) denotes the exponent of the highest power of a prime p which divides r and is referred to as the/?-adic order of r. We characterize the/?-adic orders vp(F„) and vp(Ln), i.e., the exponents of a prime/? in the prime power decomposition of Fn and Ln, respectively. The characterization of the divisibility properties of combinatorial quantities has always been

Cited by

• The p -Adic Valuation of Lucas Sequences
• The p -adic Valuations of Möbius Duals of Lucas Sequences
• The p-adic Valuations of Möbius Duals of Lucas Sequences
• On the p-adic valuation of stirling numbers of the first kind

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• The general case on the order of appearance of product of consecutive Fibonacci and Lucas numbers
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