The Order of the Fibonacci and Lucas Numbers

Abstract

In this paper vp(r) denotes the exponent of the highest power of a prime p which divides r and is referred to as the/?-adic order of r. We characterize the/?-adic orders vp(F„) and vp(Ln), i.e., the exponents of a prime/? in the prime power decomposition of Fn and Ln, respectively. The characterization of the divisibility properties of combinatorial quantities has always been