The p-Adic order of the k-Fibonacci and k-Lucas numbers |
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| Authors: | A. Kreutz J. Lelis D. Marques E. Silva P. Trojovský |
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| Affiliation: | 1.Departamento de Matemática,Universidade de Brasília,Brasília,Brazil;2.Department of Mathematics, Faculty of Science,University of Hradec Králové,Hradec Králové,Czech Republic |
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| Abstract: | 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. |
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