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.
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 ø(n), µ(n), *d(n), *s(n), r(n)
17. Generating Functions of Arithmetical Functions
18. The Order of Magnitude of Arithmetical Functions
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
List of Books
Index of Special Symbols and Words
Index of Names
Reviews from previous editions:
"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."
"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