Table of Contents

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.

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