The ass="a-plus-plus">p-Adic order of the ass="a-plus-plus">k-Fibonacci and ass="a-plus-plus">k-Lucas numbers

详细信息    查看全文

• 作者：A. Kreutz ; J. Lelis ; D. Marques ; E. Silva…
• 关键词：Key wordsk ; Fibonacci sequence ; p ; adic order ; rank of apparition of prime p in the k ; Fibonacci sequence
• 刊名：P-Adic Numbers, Ultrametric Analysis, and Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：9
• 期：1
• 页码：15-21
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra;
• 出版者：Pleiades Publishing
• ISSN：2070-0474
• 卷排序：9

文摘

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.