On Pillai's Problem involving Lucas sequences of the second kind.

In this paper, we consider the Diophantine equation V n - b m = c for given integers b ,  c with b ≥ 2 , whereas V n 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 V n .