Book:James S. Kraft/An Introduction to Number Theory with Cryptography

Subject Matter

 * Number Theory

Contents

 * Preface


 * 0 Introduction
 * 0.1. Diophantine Equations
 * 0.2. Modular Arithmetic
 * 0.3. Primes and the Distribution of Primes
 * 0.4 Cryptography


 * 1 Divisibility


 * 2 Unique Factorization


 * 3 Applications of Unique Factorization


 * 3.6 Prime Factorization of Factorials


 * 4 Congruences


 * 5 Cryptographic Applications


 * 6 Polynomial Congruences


 * 7 Order and Primitive Roots


 * 8 More Cryptographic Applications


 * 9 Quadratic Reciprocity


 * 10 Primality and Factorization


 * 11 Geometry of Numbers


 * 12 Arithmetic Functions


 * 13 Continued Fractions


 * 14 Gaussian Integers


 * 15 Algebraic Integers


 * 16 Analytic Methods


 * 17 Epilogue: Fermat's Last Theorem


 * A Supplementary Topics


 * B Answers and Hints for Odd-Numbered Exercises

Index