For an integer kβ₯2, let (Ln(k)β)nβ be the kβgeneralized
Lucas sequence which starts with 0,β¦,0,2,1 (k terms) and each term
afterwards is the sum of the k preceding terms. In this paper, we find all
the integers that appear in different generalized Lucas sequences; i.e., we
study the Diophantine equation Ln(k)β=Lm(β)β in nonnegative integers
n,k,m,β with k,ββ₯2. The proof of our main theorem uses lower
bounds for linear forms in logarithms of algebraic numbers and a version of the
Baker-Davenport reduction method. This paper is a continuation of the earlier
work [4].Comment: 14 page