The second edition of this undergraduate textbook is now available in paperback. Covering up-to-date as well as established material, it is the only textbook which deals with all the main areas of number theory, taught in the third year of a mathematics course. Each chapter ends with a collection of problems, and hints and sketch solutions are provided at the end of the book, together with useful tables.
1. Divisibility ; 2. Multiplicative Functions ; 3. Congruence Theory ; 4. Quadratic Residues ; 5. Algebraic Topics ; 6. Sums of Squares and Gauss Sums ; 7. Continued Fractions ; 8. Transcendental Numbers ; 9. Quadratic Forms ; 10. Genera and the Class Group ; 11. Partitions ; 12. The Prime Numbers ; 13. Two Major Theorems on the Primes ; 14. Diophantine Equations ; 15. Elliptic Curves: Basic Theory ; 16. Elliptic Curves: Further Results and Applications ; Answers and Hints to Problems ; Tables ; Bibliography ; Index to Notation ; General Index