On the solution of the diophantine equation G_n=p^z

Abstract

Let G_n be a second order linear recursive sequence, which satisfy certain conditions, and p be a prime. In this paper we describe an algorithm with which one can compute all but possible one integer solutions n,z of the diophantine equation G_n=p^z. In the exceptional case the algorithm gives an n such that G_n is the only possible further power of p. We give an upper bound for the running time too.

This work was written when the author was a visitor at the Universität zu Köln with the fellowship of the Alexander von Humboldt-Stiftung.