Elementary Number Theory and Its Applications / Edition 5

Elementary Number Theory and Its Applications / Edition 5

by Kenneth H. Rosen
     
 

ISBN-10: 0321237072

ISBN-13: 9780321237071

Pub. Date: 10/22/2004

Publisher: Addison Wesley

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

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Overview

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.

Product Details

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

Related Subjects

Table of Contents

Introduction1
Ch. 1The Integers
1.1Basic properties4
1.2Summations and products9
1.3Mathematical induction15
1.4Binomial coefficients28
1.5Divisibility36
1.6Representations of integers42
1.7Computer operations with integers51
1.8Complexity of integer operations57
1.9Prime numbers64
Ch. 2Greatest Common Divisors and Prime Factorization
2.1Greatest common divisors74
2.2The Euclidean algorithm80
2.3The fundamental theorem of arithmetic90
2.4Fermat numbers and factorization methods103
2.5Linear diophantine equations112
Ch. 3Congruences
3.1Introduction to congruences119
3.2Linear congruences131
3.3The Chinese remainder theorem135
3.4Systems of linear congruences145
3.5Factoring using the Pollard rho method156
Ch. 4Applications of Congruences
4.1Divisibility tests160
4.2The perpetual calendar166
4.3Round-robin tournaments171
4.4Computer file storage and hashing functions173
4.5Check digits178
Ch. 5Some Special Congruences
5.1Wilson's theorem and Fermat's little theorem185
5.2Pseudoprimes192
5.3Euler's theorem201
Ch. 6Multiplicative Functions
6.1Euler's phi-function207
6.2The sum and number of divisors217
6.3Perfect numbers and Mersenne primes223
Ch. 7Cryptology
7.1Character ciphers234
7.2Block ciphers245
7.3Exponentiation ciphers253
7.4Public-key cryptography259
7.5Knapsack ciphers266
7.6Some applications to computer science274
Ch. 8Primitive Roots
8.1The order of an integer and primitive roots278
8.2Primitive roots for primes285
8.3Existence of primitive roots290
8.4Index arithmetic298
8.5Primality testing using primitive roots308
8.6Universal exponents312
8.7Pseudo-random numbers318
8.8An application to the splicing of telephone cables324
Ch. 9Quadratic Residues and Reciprocity
9.1Quadratic residues and nonresidues331
9.2Quadratic reciprocity348
9.3The Jacobi symbol357
9.4Euler pseudoprimes367
9.5Zero-knowledge proofs377
Ch. 10Decimal Fractions and Continued Fractions
10.1Decimal fractions384
10.2Finite continued fractions394
10.3Infinite continued fractions405
10.4Periodic continued fractions417
10.5Factoring using continued fractions432
Ch. 11Some Nonlinear Diophantine Equations
11.1Pythagorean triples436
11.2Fermat's last theorem442
11.3Sums of squares447
11.4Pell's equation457
Appendix465
Answers to odd-numbered exercises481
Bibliography527
Index537

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