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. This Sixth Edition has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter 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 and the clarity of exposition is retained throughout making this textbook highly accessible to undergraduates in mathematics from the first year upwards.

Preface to the sixth editionAndrew 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 ø(n), m(n), d(n), σ(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

Godfrey H. HardyFormerly of the University of Cambridge, Edward M. WrightFormerly of the University of Aberdeen

`Review from previous edition Mathematicians of all kinds will find the book pleasant and stimulating reading, and even experts on the theory of numbers will find that the authors have something new to say on many of the topics they have selected... Each chapter is a model of clear exposition, and the notes at the ends of the chapters, with the references and suggestions for further reading, are invaluable.' Nature