Front Cover; Dedication; Contents; Preface; Chapter 0 Introduction; Chapter 1 Divisibility; Chapter 2 Unique Factorization; Chapter 3 Applications of Unique Factorization; Chapter 4 Congruences; Chapter 5 Cryptographic Applications; Chapter 6 Polynomial Congruences; Chapter 7 Order and Primitive Roots; Chapter 8 More Cryptographic Applications; Chapter 9 Quadratic Reciprocity; Chapter 10 Primality and Factorization; Chapter 11 Geometry of Numbers; Chapter 12 Arithmetic Functions; Chapter 13 Continued Fractions; Chapter 14 Gaussian Integers; Chapter 15 Algebraic Integers
Chapter 16 Analytic MethodsChapter 17 Epilogue: Fermat's Last Theorem; Appendix A Supplementary Topics; Appendix B Answers and Hints for Odd-Numbered Exercises; Back Cover
Summary
IntroductionDiophantine EquationsModular ArithmeticPrimes and the Distribution of PrimesCryptographyDivisibilityDivisibilityEuclid's Theorem Euclid's Original Proof The Sieve of Eratosthenes The Division Algorithm The Greatest Common Divisor The Euclidean Algorithm Other BasesLinear Diophantine EquationsThe Postage Stamp Problem Fermat and Mersenne Numbers Chapter Highlights Problems Unique FactorizationPreliminary Results The Fundamental Theorem of Arithmetic Euclid and the Fundamental Theorem of ArithmeticChapter Highlights Problems Applications of Unique Factorization A Puzzle Irrationality
