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.
Author(s): T. N. Shorey, R. Tijdeman
Series: Cambridge Tracts in Mathematics 87
Edition: 1
Publisher: Cambridge University Press
Year: 2008
Language: English
Pages: 252
Tags: Математика;Теория чисел;
Cambridge Tracts in Mathematics 87......Page 2
Exponential diophantine equations......Page 4
9780521268264......Page 5
Contents......Page 8
Introduction......Page 12
Notation......Page 16
A. Results from algebraic number theory......Page 20
B. Estimates of linear forms in logarithms......Page 40
C. Recurrence sequences......Page 43
1. Purely exponential equations......Page 51
2. Binary recurrence sequences with rational roots......Page 67
3. Binary recurrence sequences......Page 74
4. Recurrence sequences of order 2, 3 and 4......Page 93
5. The Thue equation......Page 110
6. The superelliptic equation......Page 124
7. The Thue-Mahler equation......Page 135
8. The generalised superelliptic equation......Page 152
9. Perfect powers in binary recurrence sequences......Page 161
10. Perfect powers at integral values of a polynomial......Page 180
11. The Fermat equation......Page 195
12. The Catalan equation and related equations......Page 212
References......Page 232
Index......Page 250
