The downloadable files below, in PDF format, contain answers to the exercises from chapters 1 - 9 of the 5th edition. To download any exercise to your computer, click on the appropriate file. Then, to view the file contents, double-click on the file.

All of the individual files below are combined into one file (64 MB), which can be downloaded by clicking on the below link.

4 The Diophantine Equation ax+by=c

1 The Fundamental Theorem of Arithmetic

2 Basic Properties of Congruence

2 Fermat's Factorization Method

2 The Mobius Inversion Formula

3 The Greatest Integer Function

4 An Application to the Calendar

3 Euler's Generalization of Fermat's Theorem

4 Some Properties of the Phi-Function

5 An Application to Cryptography

1 The Order of an Integer Modulo n

3 Composite Numbers Having Primitive Roots

2 The Legendre Symbol and Its Properties

4 Quadratic Congruences With Composite Moduli