| Credits | |
| Preface | |
| What Is Number Theory? | 1 |
| 1 | Divisibility | 13 |
| 1.1 | The GCD and LCM | 13 |
| 1.2 | The Division Algorithm | 18 |
| 1.3 | The Euclidean Algorithm | 23 |
| 1.4 | Linear Combinations | 27 |
| 1.5 | Congruences | 33 |
| 1.6 | Mathematical Induction | 38 |
| 2 | Prime Numbers | 47 |
| 2.1 | Prime Factorization | 47 |
| 2.2 | The Fundamental Theorem of Arithmetic | 52 |
| 2.3 | The Importance of Unique Factorization | 55 |
| 2.4 | Prime Power Factorizations | 60 |
| 2.5 | The Set of Primes is Infinite | 65 |
| 2.6 | A Formula for [tau](n) | 71 |
| 3 | Numerical Functions | 77 |
| 3.1 | The Sum of the Divisors | 77 |
| 3.2 | Multiplicative Functions | 83 |
| 3.3 | Perfect Numbers | 90 |
| 3.4 | Mersenne and Fermat Numbers | 94 |
| 3.5 | The Euler Phi Function | 101 |
| 3.6 | The Mobius Inversion Formula | 108 |
| 4 | The Algebra of Congruence Classes | 117 |
| 4.1 | Solving Linear Congruences | 117 |
| 4.2 | The Clinese Remainder Theorem | 125 |
| 4.3 | The Theorems of Fermat and Euler | 133 |
| 4.4 | Primality Testing | 140 |
| 4.5 | Public-Key Cryptography | 148 |
| 5 | Congruences of Higher Degree | 159 |
| 5.1 | Polynomial Congruences | 159 |
| 5.2 | Congruences with Prime Power Moduli | 165 |
| 5.3 | Quadratic Residues | 172 |
| 5.4 | Quadratic Reciprocity | 179 |
| 5.5 | Flipping a Coin over the Telephone | 186 |
| 6 | The Number Theory of the Reals | 195 |
| 6.1 | Rational and Irrational Numbers | 195 |
| 6.2 | Finite Continued Fractions | 203 |
| 6.3 | Infinite Continued Fractions | 211 |
| 6.4 | Decimal Representation | 220 |
| 6.5 | Lagrange's Theorem and Primitive Roots | 226 |
| 7 | Diophantine Equations | 235 |
| 7.1 | Pythagorean Triples | 235 |
| 7.2 | Sums of Two Squares | 242 |
| 7.3 | Sums of Four Squares | 247 |
| 7.4 | Sums of Fourth Powers | 251 |
| 7.5 | Pell's Equation | 256 |
| Bibliography | 263 |
| Answers to Odd-Numbered Problems | 267 |
| Index | 275 |
Format: Textbook Hardcover - LARGE PRI
