On the solution of the diophantine equation Gn=pz

  • Attila Pethö
Computational Number Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


Let Gn 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 Gn=pz. In the exceptional case the algorithm gives an n such that Gn is the only possible further power of p. We give an upper bound for the running time too.


Ideal Factor Integer Solution Diophantine Equation Acta Arith Recursive Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Attila Pethö
    • 1
  1. 1.Mathematical InstituteKossuth Lajos UniversityDebrecenHungary

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