Diophantine properties of linear recursive sequences II

Abstract

Let Gn be a linear recursive sequence of integers and P(y) be a polynomial with integer coefficients. In this paper we are given a survey on results on the solutions of diophantine equation Gn = P(y). We prove especially that if Gn is of order three such that its characteristic polynomial is irreducible and has a dominating root then there are only finitely many perfect powers in Gn.