Elementary Number Theory and Its Applications / Edition 4

Elementary Number Theory and Its Applications / Edition 4

by Kenneth H. Rosen
     
 

ISBN-10: 0201870738

ISBN-13: 9780201870732

Pub. Date: 01/06/2000

Publisher: Pearson

This latest edition of Kenneth Rosen's widely used Elementary Number Theory and Its Applications enhances the flexibility and depth of previous editions while preserving their strengths. Rosen effortlessly blends classic theory with contemporary applications. New examples, additional applications and increased cryptology coverage are also included.

Overview

This latest edition of Kenneth Rosen's widely used Elementary Number Theory and Its Applications enhances the flexibility and depth of previous editions while preserving their strengths. Rosen effortlessly blends classic theory with contemporary applications. New examples, additional applications and increased cryptology coverage are also included. The book has also been accuracy-checked to ensure the quality of the content. A diverse group of exercises are presented to help develop skills. Also included are computer projects. The book contains updated and increased coverage of Cryptography and new sections on Mvbius Inversion and solving Polynomial Congruences. Historical content has also been enhanced to show the history for the modern material. For those interested in number theory.

Product Details

ISBN-13:
9780201870732
Publisher:
Pearson
Publication date:
01/06/2000
Edition description:
Older Edition
Pages:
544
Product dimensions:
6.50(w) x 9.00(h) x 1.40(d)

Related Subjects

Table of Contents

P. What is Number Theory?

1. The Integers.

Numbers and Sequences.

Sums and Products.

Mathematical Induction.

The Fibonacci Numbers.

2. Integer Representations and Operations.

Representations of Integers.

Computer Operations with Integers.

Complexity of Integer Operations.

3. Primes and Greatest Common Divisors.

Prime Numbers.

The Distribution of Primes.

Greatest Common Divisors.

The Euclidean Algorithm.

The Fundemental Theorem of Arithmetic.

Factorization Methods and Fermat Numbers.

Linear Diophantine Equations.

4. Congruences.

Introduction to Congruences.

Linear Congrences.

The Chinese Remainder Theorem.

Solving Polynomial Congruences.

Systems of Linear Congruences.

Factoring Using the Pollard Rho Method.

5. Applications of Congruences.

Divisibility Tests.

The perpetual Calendar.

Round Robin Tournaments.

Hashing Functions.

Check Digits.

6. Some Special Congruences.

Wilson's Theorem and Fermat's Little Theorem.

Pseudoprimes.

Euler's Theorem.

7. Multiplicative Functions.

The Euler Phi-Function.

The Sum and Number of Divisors.

Perfect Numbers and Mersenne Primes.

Mobius Inversion.

8. Cryptology.

Character Ciphers.

Block and Stream Ciphers.

Exponentiation Ciphers.

Knapsack Ciphers.

Cryptographic Protocols and Applications.

9. Primitive Roots.

The Order of an Integer and Primitive Roots.

Primitive Roots for Primes.

The Existence of Primitive Roots.

Index Arithmetic.

Primality Tests Using Orders of Integers and Primitive Roots.

Universal Exponents.

10. Applications of Primitive Roots and the Order of an Integer.

Pseudorandom Numbers.

The EIGamal Cryptosystem.

An Application to the Splicing of Telephone Cables.

11. Quadratic Residues.

Quadratic Residues and nonresidues.

The Law of Quadratic Reciprocity.

The Jacobi Symbol.

Euler Pseudoprimes.

Zero-Knowledge Proofs.

12. Decimal Fractions and Continued.

Decimal Fractions.

Finite Continued Fractions.

Infinite Continued Fractions.

Periodic Continued Fractions.

Factoring Using Continued Fractions.

13. Some Nonlinear Diophantine Equations.

Pythagorean Triples.

Fermat's Last Theorem.

Sums of Squares.

Pell's Equation.

14. The Gaussian Integers.

Gaussian Primes.

Unique Factorization of Gaussian Integers.

Gaussian Integers and Sums of Squares.

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