1. Introduction. 2. Preliminaries. 3. Divisibility. 4. Prime numbers and their distribution. 5. Congruences. 6. Factorization, Fermat's and Wilson's theorem. 7. Arithmetic functions. 8. Primitive roots. 9. Quadratic congruences. 10. Perfect numbers et. al. 11. Sum of squares. 12. Partitions. 13. Fibonacci and Farey sequences. 14. Some applications.
An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text.
In addition, the book discusses applications of number theory to cryptography in a very readable fashion, with any additional mathematics required for the book (in this case some simple group theory and analysis) in two appendices. A book on number theory would also be incomplete without at least a brief discussion of Andrew Wiles and Fermat's last theorem.
This book provides a brisk, thorough treatment of the foundations of algebraic number theory on which it builds to introduce more advanced topics. Throughout, the authors emphasize the systematic development of techniques for the explicit calculation. (jacket)