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

James S. Kraft and Lawrence C. Washington: An Introduction to Number Theory with Cryptography

Published $\text {2013}$, Taylor & Francis Group, LLC

ISBN 978-1482214413

Subject Matter

• Number Theory

Contents

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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