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.

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".

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