The Order of the Fibonacci and Lucas Numbers

1995/06/01 by T. Lengyel, Tamás Lengyel · 3 citations
Physics and Astronomy · Mathematics · #Advanced Mathematical Theories and Applications #Advanced Mathematical Identities #Mathematics and Applications

paper · doi:10.1080/00150517.1995.12429139

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

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• The <i>p</i> -Adic Valuation of Lucas Sequences
• The <i>p</i> -adic Valuations of Möbius Duals of Lucas Sequences
• The p-adic Valuations of Möbius Duals of Lucas Sequences

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