Author(s)

Ari Heimonen

Abstract

The paper gives a computational method for solving Diophantine equa- tions aa;^ - 6^^ = K for certain a, 6 and A". The method is based on an effective irrationality measure result for \/a/b and on the computation of the continued fraction expansion of $/a/b up to 20 000 partial denomina- tors. The computation was performed using MATHEMATICA. 1 Introduction Thue [17] showed in 1919 that we can find an upper bound for all the integer solutions of the equation or correspondingly, of the inequality |a^-&2/| Keywords