Abstract
In this paper, we consider the Diophantine equation Vn - bm = c for given integers b, c with b ≥ 2, whereas Vn varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation has at least three solutions (n, m) , then there is an upper bound on the size of the solutions as well as on the size of the coefficients in the characteristic polynomial of Vn.