Abstract
A generalization of the well-known Fibonacci sequence is the k-generalized Fibonacci sequence (Fn(k))n≥2−k for some integer k≥2, whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. In this paper, we look at the prime factors of the reduced rational number Fn(k)/Fm(ℓ) as max{m,n,k,ℓ} tends to infinity.
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