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| Preface | |
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| A Word to the Student | |
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| Fundamentals | |
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| Fundamental Properties | |
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| The Summation and Product Notations | |
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| Mathematical Induction | |
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| Recursion | |
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| The Binomial Theorem | |
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| Polygonal Numbers | |
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| Pyramidal Numbers | |
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| Catalan Numbers | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Divisibility | |
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| The Division Algorithm | |
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| Base-b Representations (optional) | |
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| Operations in Nondecimal Bases (optional) | |
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| Number Patterns | |
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| Prime and Composite Numbers | |
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| Fibonacci and Lucas Numbers | |
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| Fermat Numbers | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Greatest Common Divisors | |
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| Greatest Common Divisor | |
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| The Euclidean Algorithm | |
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| The Fundamental Theorem of Arithmetic | |
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| Least Common Multiple | |
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| Linear Diophantine Equations | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Congruences | |
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| Congruences | |
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| Linear Congruences | |
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| The Pollard Rho Factoring Method | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Congruence Applications | |
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| Divisibility Tests | |
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| Modular Designs | |
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| Check Digits | |
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| The p-Queens Puzzle (optional) | |
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| Round-Robin Tournaments (optional) | |
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| The Perpetual Calendar (optional) | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Systems of Linear Congruences | |
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| The Chinese Remainder Theorem | |
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| General Linear Systems (optional) | |
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| 2 x 2 Linear Systems (optional) | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Three Classical Milestones | |
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| Wilson's Theorem | |
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| Fermat's Little Theorem | |
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| Pseudoprimes (optional) | |
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| Euler's Theorem | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Multiplicative Functions | |
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| Euler's Phi Function Revisited | |
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| The Tau and Sigma Functions | |
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| Perfect Numbers | |
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| Mersenne Primes | |
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| The Mobius Function (optional) | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Cryptology | |
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| Affine Ciphers | |
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| Hill Ciphers | |
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| Exponentiation Ciphers | |
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| The RSA Cryptosystem | |
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| Knapsack Ciphers | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Primitive Roots and Indices | |
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| The Order of a Positive Integer | |
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| Primality Tests | |
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| Primitive Roots for Primes | |
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| Composites with Primitive Roots (optional) | |
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| The Algebra of Indices | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Quadratic Congruences | |
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| Quadratic Residues | |
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| The Legendre Symbol | |
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| Quadratic Reciprocity | |
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| The Jacobi Symbol | |
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| Quadratic Congruences with Composite Moduli (optional) | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Continued Fractions | |
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| Finite Continued Fractions | |
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| Infinite Continued Fractions | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Miscellaneous Nonlinear Diophantine Equations | |
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| Pythagorean Triangles | |
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| Fermat's Last Theorem | |
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| Sums of Squares | |
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| Pell's Equation | |
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| Chapter Summary | |
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| Review Exercises | |
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| Supplementary Exercises | |
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| Computer Exercises | |
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| Enrichment Readings | |
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| Appendix | |
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| Proof Methods | |
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| Web Sites | |
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| Tables | |
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| Factor Table | |
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| Values of Some Arithmetic Functions | |
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| Least Primitive Roots r Modulo Primes p | |
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| Indices | |
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| References | |
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| Solutions to Odd-Numbered Exercises | |
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| Fundamentals | |
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| Divisibility | |
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| Greatest Common Divisors | |
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| Congruences | |
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| Congruence Applications | |
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| Systems of Linear Congruences | |
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| Three Classical Milestones | |
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| Multiplicative Functions | |
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| Cryptology | |
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| Primitive Roots and Indices | |
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| Quadratic Congruences | |
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| Continued Fractions | |
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| Miscellaneous Nonlinear Diophantine Equations | |
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| Credits | |
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| Index | |