Exponential Diophantine Equations

This is a integrated presentation of the theory of exponential diophantine equations.

T. N. Shorey (Author), R. Tijdeman (Author)

9780521091701, Cambridge University Press

Paperback / softback, published 4 December 2008

252 pages
22.9 x 15.2 x 1.5 cm, 0.38 kg

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.

Part I. Preliminaries: Part II. Diophantine equations and recurrence sequences: 1. Purely exponential equations
2. Binary recurrence sequences with rational roots
3. Binary recurrence sequences
4. Recurrence sequences of order 2, 3 and 4
5. The Thue equation
6. The superelliptic equation
7. The Thue-Mahler equation
8. The generalised superelliptic equation
9. Perfect powers in binary recurrence sequences
10. Perfect powers at integral values of a polynomial
11. The Fermat equation
12. The Catalan equation and related equations.

Subject Areas: Algebra [PBF]