ISBN13: 978-3540761976

ISBN10: 3540761977

Cover type:

Edition/Copyright: 98

Publisher: Springer-Verlag New York

Published: 1998

International: No

ISBN10: 3540761977

Cover type:

Edition/Copyright: 98

Publisher: Springer-Verlag New York

Published: 1998

International: No

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This book gives an undergraduate-level introduction to Number Theory with the emphasis on fully explained proofs and examples; exercises (with solutions) are integrated into the text. The first few chapters covering divisibility prime numbers and modular arithmetic assume only basic school algebra and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) are then used to study groups of units quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part suitable for third-year students uses ideas from algebra analysis calculus and geometry to study Dirichlet series and sums of squares; in particular the last chapter gives a concise account of Fermat's Last Theorem from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

Preface

Notes to the reader

Divisibility

Prime Numbers

Congruences

Congruences with prime modulus

Euler's function

The group of units

Quadratic residues

Arithmetic functions

The Riemann zeta function

Sums of squares

Fermat's Last Theorem

Appendix 1: Induction and well-ordering

Appendix 2: Groups rings and fields

Appendix 3: Convergence

Table of primes

Solutions to excercises

References

Index of symbols

Index of names

Index.

ISBN10: 3540761977

Cover type:

Edition/Copyright: 98

Publisher: Springer-Verlag New York

Published: 1998

International: No

This book gives an undergraduate-level introduction to Number Theory with the emphasis on fully explained proofs and examples; exercises (with solutions) are integrated into the text. The first few chapters covering divisibility prime numbers and modular arithmetic assume only basic school algebra and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) are then used to study groups of units quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part suitable for third-year students uses ideas from algebra analysis calculus and geometry to study Dirichlet series and sums of squares; in particular the last chapter gives a concise account of Fermat's Last Theorem from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

Table of Contents

Notes to the reader

Divisibility

Prime Numbers

Congruences

Congruences with prime modulus

Euler's function

The group of units

Quadratic residues

Arithmetic functions

The Riemann zeta function

Sums of squares

Fermat's Last Theorem

Appendix 1: Induction and well-ordering

Appendix 2: Groups rings and fields

Appendix 3: Convergence

Table of primes

Solutions to excercises

References

Index of symbols

Index of names

Index.

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