This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations. The necessary preliminaries are given in the first three chapters. Each chapter ends with a section giving details of related results.

No abstract

No abstract

1. Introduction. Let b, d, , n and y be positive integers such that gcd(n, d) = 1 and > 2 is a prime number. Let k ≥ 2, t ≥ 2 and r ∈ {0, 1} be integers satisfying t = k − r. Thus k ≥ 2 if r = 0 and k ≥ 3 if r = 1. Let d 1 < . . . < d t be integers in the interval [0, k). We write

No abstract