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Exponential Diophantine Equations

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Exponential Diophantine Equations

Exponential Diophantine Equations

T. N. Shorey
R. Tijdeman
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9780511869723
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    Description

    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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    Contents

    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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    About the authors
      Authors
    • T. N. Shorey
    • R. Tijdeman

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