The  p -Adic order of the  k -Fibonacci and  k -Lucas numbers

A. Kreutz; J. Lelis; D. Marques; E. Silva; P. Trojovský

doi:10.1134/S2070046617010022

The p-Adic order of the k-Fibonacci and k-Lucas numbers

作者: Kreutz A.¹, Lelis J.¹, Marques D.¹, Silva E.¹, Trojovský P.²
隶属关系:
1. Departamento de Matemática
2. Department of Mathematics, Faculty of Science
期: 卷 9, 编号 1 (2017)
页面: 15-21
栏目: Research Articles
URL: https://journals.rcsi.science/2070-0466/article/view/200707
DOI: https://doi.org/10.1134/S2070046617010022
ID: 200707

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详细

Let (F_k,n)_n and (L_k,n)n be the k-Fibonacci and k-Lucas sequence, respectively, which satisfies the same recursive relation a_n+1 = ka_n + a_n−1 with initial values F_k,0 = 0, F_k,1 = 1, L_k,0 = 2 and L_k,1 = k. In this paper, we characterize the p-adic orders ν_p(F_k,n) and ν_p(L_k,n) for all primes p and all positive integers k.