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On The Least Significant P-Adic Digits Of Certain Lucas Numbers, Tamas Lengyel
On The Least Significant P-Adic Digits Of Certain Lucas Numbers, Tamas Lengyel
Tamas Lengyel
We calculate the least significant p-ary digits of certain Lucas numbers Vn = Vn(P,Q)withV0 =2,V1 =PandVn =PVn1QVn2 forn2. Webase our study on an observation regarding these numbers: as m increases, more and more p-adic digits match in Vkpm with integer k 1. We use multi-section identities for generating functions and derive congruences for the underlying sequences.