Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 17, No. 2, pp. 81-96 (2001)

Diophantine properties of linear recursive sequences II

Attila Pethő

Institut for Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, PO Box 12, Hungary pethoe@math.klte.hu

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

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