An Introduction to the Theory of Numbers

• Much-needed update of a classic text
• Extensive end-of-chapter notes
• Suggestions for further reading for the more avid reader
• New chapter on one of the most important developments in number theory and its role in the proof of Fermat's Last Theorem

New to this edition

• Revised end-of-chapter notes
• New chapter on elliptic curves

Readership: Undergraduates in mathematics, sepcifically number theory and algebra.

Godfrey H. Hardy, Formerly of the University of Cambridge, and Edward M. Wright, Formerly of the University of Aberdeen

Review(s) 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

"This fascinating book... gives a full, vivid and exciting account of its subject, as far as this can be done without using too much advanced theory." - Mathematical Gazette

"...an important reference work... which is certain to continue its long and successful life..." - Mathematical Reviews

"...remains invaluable as a first course on the subject, and as a source of food for thought for anyone wishing to strike out on his own." - Matyc Journal

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), µ(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: Joseph H. Silverman: Elliptic Curves
Appendix
List of Books
Index of Special Symbols and Words
Index of Names
General Index