**An Introduction to the Theory of Numbers 6th Edition by G. H. Hardy, ISBN-13: 978-0199219865**

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- Publisher: Oxford University Press; 6th edition (September 15, 2008)
- Language: English
- 621 pages
- ISBN-10: 9780199219865
- ISBN-13: 978-0199219865

* An Introduction to the Theory of Numbers* by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today’s students through the key milestones and developments in number theory.

Updates include a chapter by J. H. Silverman on one of the most important developments in number theory – modular elliptic curves and their role in the proof of Fermat’s Last Theorem — a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader.

The text retains the style and clarity of previous editions making it highly suitable for undergraduates in * mathematics* from the first year upwards as well as an essential reference for all number theorists.

**Table of Contents:**

Preface to the sixth edition Andrew Wiles

Preface to the fifth edition

1. The Series of Primes (1)

2. The Series of Primes (2)

3. Farey Series and a Theorem of Minkowski

4. Irrational Numbers

5. Congruences and Residues

6. Fermat’s Theorem and its Consequences

7. General Properties of Congruences

8. Congruences to Composite Moduli

9. The Representation of Numbers by Decimals

10. Continued Fractions

11. Approximation of Irrationals by Rationals

12. The Fundamental Theorem of **Arithmetic** in k(l), k(i), and k(p)

13. Some Diophantine Equations

14. Quadratic Fields (1)

15. Quadratic Fields (2)

16. The Arithmetical Functions Ã¸(n), Âµ(n), *d(n), *s(n), r(n)

17. Generating Functions of Arithmetical Functions

18. The Order of Magnitude of Arithmetical Functions

19. Partitions

20. The Representation of a Number by Two or Four Squares

21. Representation by Cubes and Higher Powers

22. The Series of Primes (3)

23. Kronecker’s Theorem

24. Geometry of Numbers

25. Elliptic Curves, Joseph H. Silverman

Appendix

List of Books

Index of Special Symbols and Words

Index of Names

General Index

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