Abstract: Let $G_n$ 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 $G_n=P(y)$. We prove especially that if $G_n$ 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 $G_n$.
Keywords: Linear recursive sequence, characteristic polynomial. Linear forms in logarithms of algebraic numbers, subspace theorem.
Classification (MSC2000): 11D61; 11D25
Full text of the article: