Exponential Diophantine Equations

T. N. Shorey; R. Tijdeman

doi:10.1017/CBO9780511566042

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.

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Exponential Diophantine Equations

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-x

Introduction
pp 1-4

Notation
pp 5-8

Preliminaries

A - Results from algebraic number theory
pp 9-28

B - Estimates of linear forms in logarithms
pp 29-31

C - Recurrence sequences
pp 32-39

Diophantine equations and recurrence sequences

1 - Purely exponential equations
pp 40-55

2 - Binary recurrence sequences with rational roots
pp 56-62

3 - Binary recurrence sequences
pp 63-81

4 - Recurrence sequences of order 2, 3 and 4
pp 82-98

5 - The Thue equation
pp 99-112

6 - The superelliptic equation
pp 113-123

7 - The Thue–Mahler equation
pp 124-140

8 - The generalised superelliptic equation
pp 141-149

9 - Perfect powers in binary recurrence sequences
pp 150-168

10 - Perfect powers at integral values of a polynomial
pp 169-183

11 - The Fermat equation
pp 184-200

12 - The Catalan equation and related equations
pp 201-220

References
pp 221-238

Index
pp 239-240

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Exponential Diophantine Equations

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