Elementary Number Theory and Its Applications / Edition 5

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Elementary Number Theory and Its Applications is noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises.

The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years.

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Editorial Reviews

New edition of a standard text. Integrates classical material with applications to cryptography and computer science. The author is with AT&T Bell Labs. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780321237071
  • Publisher: Addison Wesley
  • Publication date: 10/22/2004
  • Series: Alternative eText Formats Series
  • Edition description: REV
  • Edition number: 5
  • Pages: 719
  • Product dimensions: 7.01 (w) x 9.10 (h) x 1.38 (d)

Table of Contents

Introduction 1
Ch. 1 The Integers
1.1 Basic properties 4
1.2 Summations and products 9
1.3 Mathematical induction 15
1.4 Binomial coefficients 28
1.5 Divisibility 36
1.6 Representations of integers 42
1.7 Computer operations with integers 51
1.8 Complexity of integer operations 57
1.9 Prime numbers 64
Ch. 2 Greatest Common Divisors and Prime Factorization
2.1 Greatest common divisors 74
2.2 The Euclidean algorithm 80
2.3 The fundamental theorem of arithmetic 90
2.4 Fermat numbers and factorization methods 103
2.5 Linear diophantine equations 112
Ch. 3 Congruences
3.1 Introduction to congruences 119
3.2 Linear congruences 131
3.3 The Chinese remainder theorem 135
3.4 Systems of linear congruences 145
3.5 Factoring using the Pollard rho method 156
Ch. 4 Applications of Congruences
4.1 Divisibility tests 160
4.2 The perpetual calendar 166
4.3 Round-robin tournaments 171
4.4 Computer file storage and hashing functions 173
4.5 Check digits 178
Ch. 5 Some Special Congruences
5.1 Wilson's theorem and Fermat's little theorem 185
5.2 Pseudoprimes 192
5.3 Euler's theorem 201
Ch. 6 Multiplicative Functions
6.1 Euler's phi-function 207
6.2 The sum and number of divisors 217
6.3 Perfect numbers and Mersenne primes 223
Ch. 7 Cryptology
7.1 Character ciphers 234
7.2 Block ciphers 245
7.3 Exponentiation ciphers 253
7.4 Public-key cryptography 259
7.5 Knapsack ciphers 266
7.6 Some applications to computer science 274
Ch. 8 Primitive Roots
8.1 The order of an integer and primitive roots 278
8.2 Primitive roots for primes 285
8.3 Existence of primitive roots 290
8.4 Index arithmetic 298
8.5 Primality testing using primitive roots 308
8.6 Universal exponents 312
8.7 Pseudo-random numbers 318
8.8 An application to the splicing of telephone cables 324
Ch. 9 Quadratic Residues and Reciprocity
9.1 Quadratic residues and nonresidues 331
9.2 Quadratic reciprocity 348
9.3 The Jacobi symbol 357
9.4 Euler pseudoprimes 367
9.5 Zero-knowledge proofs 377
Ch. 10 Decimal Fractions and Continued Fractions
10.1 Decimal fractions 384
10.2 Finite continued fractions 394
10.3 Infinite continued fractions 405
10.4 Periodic continued fractions 417
10.5 Factoring using continued fractions 432
Ch. 11 Some Nonlinear Diophantine Equations
11.1 Pythagorean triples 436
11.2 Fermat's last theorem 442
11.3 Sums of squares 447
11.4 Pell's equation 457
Appendix 465
Answers to odd-numbered exercises 481
Bibliography 527
Index 537
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Sort by: Showing all of 2 Customer Reviews
  • Anonymous

    Posted July 31, 2005

    there are better number theory books out there

    there are better number theory books out there with better examples. my professors was rather dry .. with a better teacher this book may have seemed a little bit better to me. I ended up using the internet as a study source and a used copy i found online of Elementary Number Theory by David M. Burton

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  • Anonymous

    Posted February 20, 2010

    No text was provided for this review.

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