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.

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

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