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Elementary Number Theory and Its Applications
ISBN: 9780201578898 | 0201578891
Edition: 3rdFormat: Hardcover
Publisher: Addison-Wesley
Pub. Date: 1/1/1992
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| Introduction | p. 1 |
| The Integers | |
| Basic properties | p. 4 |
| Summations and products | p. 9 |
| Mathematical induction | p. 15 |
| Binomial coefficients | p. 28 |
| Divisibility | p. 36 |
| Representations of integers | p. 42 |
| Computer operations with integers | p. 51 |
| Complexity of integer operations | p. 57 |
| Prime numbers... MORE | p. 64 |
| Greatest Common Divisors and Prime Factorization | |
| Greatest common divisors | p. 74 |
| The Euclidean algorithm | p. 80 |
| The fundamental theorem of arithmetic | p. 90 |
| Fermat numbers and factorization methods | p. 103 |
| Linear diophantine equations | p. 112 |
| Congruences | |
| Introduction to congruences | p. 119 |
| Linear congruences | p. 131 |
| The Chinese remainder theorem | p. 135 |
| Systems of linear congruences | p. 145 |
| Factoring using the Pollard rho method | p. 156 |
| Applications of Congruences | |
| Divisibility tests | p. 160 |
| The perpetual calendar | p. 166 |
| Round-robin tournaments | p. 171 |
| Computer file storage and hashing functions | p. 173 |
| Check digits | p. 178 |
| Some Special Congruences | |
| Wilson's theorem and Fermat's little theorem | p. 185 |
| Pseudoprimes | p. 192 |
| Euler's theorem | p. 201 |
| Multiplicative Functions | |
| Euler's phi-function | p. 207 |
| The sum and number of divisors | p. 217 |
| Perfect numbers and Mersenne primes | p. 223 |
| Cryptology | |
| Character ciphers | p. 234 |
| Block ciphers | p. 245 |
| Exponentiation ciphers | p. 253 |
| Public-key cryptography | p. 259 |
| Knapsack ciphers | p. 266 |
| Some applications to computer science | p. 274 |
| Primitive Roots | |
| The order of an integer and primitive roots | p. 278 |
| Primitive roots for primes | p. 285 |
| Existence of primitive roots | p. 290 |
| Index arithmetic | p. 298 |
| Primality testing using primitive roots | p. 308 |
| Universal exponents | p. 312 |
| Pseudo-random numbers | p. 318 |
| An application to the splicing of telephone cables | p. 324 |
| Quadratic Residues and Reciprocity | |
| Quadratic residues and nonresidues | p. 331 |
| Quadratic reciprocity | p. 348 |
| The Jacobi symbol | p. 357 |
| Euler pseudoprimes | p. 367 |
| Zero-knowledge proofs | p. 377 |
| Decimal Fractions and Continued Fractions | |
| Decimal fractions | p. 384 |
| Finite continued fractions | p. 394 |
| Infinite continued fractions | p. 405 |
| Periodic continued fractions | p. 417 |
| Factoring using continued fractions | p. 432 |
| Some Nonlinear Diophantine Equations | |
| Pythagorean triples | p. 436 |
| Fermat's last theorem | p. 442 |
| Sums of squares | p. 447 |
| Pell's equation | p. 457 |
| Appendix | p. 465 |
| Answers to odd-numbered exercises | p. 481 |
| Bibliography | p. 527 |
| Index | p. 537 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
