ABSTRACT

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the tex

chapter |8 pages

Introduction

chapter 1|46 pages

- Divisibility

chapter 2|12 pages

- Linear Diophantine Equations

chapter 3|10 pages

- Unique Factorization

chapter 4|18 pages

- Applications of Unique Factorization

chapter 5|38 pages

- Congruences

chapter 6|20 pages

- Fermat, Euler, Wilson

chapter 7|46 pages

- Cryptographic Applications

chapter 8|30 pages

- Order and Primitive Roots

chapter 9|16 pages

- More Cryptographic Applications

chapter 10|30 pages

- Quadratic Reciprocity

chapter 11|22 pages

- Primality and Factorization

chapter 12|14 pages

- Sums of Squares

chapter 13|16 pages

- Arithmetic Functions

chapter 14|14 pages

- Continued Fractions

chapter 15|10 pages

- Recent Developments