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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Kreutz, A., Lelis, J., Marques, D. et al. The p-Adic order of the k-Fibonacci and k-Lucas numbers. P-Adic Num Ultrametr Anal Appl 9, 15–21 (2017). https://doi.org/10.1134/S2070046617010022
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DOI: https://doi.org/10.1134/S2070046617010022