American River Software

Elementary Number Theory Cover  Elementary Number Theory, by David M. Burton

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.

Combined Solutions

Chapter 1 - Some Preliminary Considerations

1 Mathematical Induction

2 The Binomial Theorem

3 Early Number Theory

Chapter 2 - Divisibility Theory in the Integers

1 The Division Algorithm

2 The Greatest Common Divisor

3 The Euclidean Algorithm

4 The Diophantine Equation ax+by=c

Chapter 3 - Primes and Their Distribution

1 The Fundamental Theorem of Arithmetic

2 The Sieve of Eratosthenes

3 The Goldbach Conjecture

Chapter 4 - The Theory of Congruences

2 Basic Properties of Congruence

3 Special Divisibility Tests

4 Linear Congruences

Chapter 5 - Fermat's Theorem

2 Fermat's Factorization Method

3 The Little Theorem

4 Wilson's Theorem

Chapter 6 - Number-Theoretic Functions

1 The Functions tau and sigma

2 The Mobius Inversion Formula

3 The Greatest Integer Function

4 An Application to the Calendar

Chapter 7 - Euler's Generalization of Fermat's Theorem

2 Euler's Phi Function

3 Euler's Generalization of Fermat's Theorem

4 Some Properties of the Phi-Function

5 An Application to Cryptography

Chapter 8 - Primitive Roots and Indices

1 The Order of an Integer Modulo n

2 Primitive Roots for Primes

3 Composite Numbers Having Primitive Roots

4 The Theory of Indices

Chapter 9 - The Quadratic Reciprocity Law

1 Euler's Criterion

2 The Legendre Symbol and Its Properties

3 Quadratic Reciprocity

4 Quadratic Congruences With Composite Moduli