Book:David M. Burton/Elementary Number Theory/Revised Printing

Subject Matter

 * Number Theory

Contents

 * Preface


 * Chapter 1. Some Preliminary Considerations
 * 1.1 Mathematical Induction
 * 1.2 The Binomial Theorem
 * 1.3 Early Number Theory


 * Chapter 2. Divisibility Theory in the Integers
 * 2.1 The Division Algorithm
 * 2.2 The Greatest Common Divisor
 * 2.3 The Euclidean Algorithm
 * 2.4 The Diophantine Equation $a x + b y = c$


 * Chapter 3. Primes and Their Distribution


 * Chapter 4. The Theory of Congruences


 * Chapter 5. Fermat's Theorem


 * Chapter 6. Number Theoretic Functions


 * Chapter 7. Euler's Generalization of Fermat's Theorem


 * Chapter 8. Primitive Roots and Indices


 * Chapter 9. The Quadratic Reciprocity Law


 * Chapter 10. Perfect Numbers


 * Chapter 11. The Fermat Conjecture


 * Chapter 12. Representation of Integers as Sums of Squares


 * Chapter 13. Fibonacci Numbers and Continued Fractions


 * Appendices.
 * The Prime Number Theorem
 * References
 * Suggestions for Further Reading
 * Tables
 * Answers to Selected Problems
 * Index



Source work progress
* : Chapter $2$: Divisibility Theory in the Integers: $2.2$ The Greatest Common Divisor: Problems $2.2$: $15 \ \text {(c)}$