Elementary Number Theory and Its Applications

by Rosen, Kenneth H.

• ISBN13: 9780201870732
• ISBN10: 0201870738
• Edition: 4th
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Addison Wesley

Summary

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 Historical content has also been enhanced to show the history for the modern material.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.

Table of Contents

The Integers

Numbers, Sequences, and Sums

Mathematical Induction

The Fibonacci Numbers

Divisibility

Integer Representation and Operations

Representation of Integers

Computer Operations with Integers

Complexity of Integer Operations

Primes and Greatest Common Divisors

Prime Numbers

Greatest Common Divisors

The Euclidean Algorithm

The Fundamental Theorem of Arithmetic

Factorization Methods and the Fermat Numbers

Linear Diophantine Equations

Congruences

Introduction to Congruences

Linear Congruences

The Chinese Remainder Theorem

Solving Polynomial Congruences

Systems of Linear Congruences

Factoring Using the Pollard rho Method

Applications of Congruences

Divisibility Tests

The Perpetual Calendar

Round-Robin Tournaments

Hashing Functions

Check Digits

Some Special Congruences

Wilson's Theorem and Fermat's Little Theorem

Pseudoprimes

Euler's Theorem

Multiplicative Functions

Euler's Phi-Function

The Sum and Number of Divisors

Perfect Numbers and Mersenne Primes

Mouml;bius Inversion

Cryptology

Character Ciphers

Block and Stream Ciphers

Exponentiation Ciphers

Public-Key Crytography

Knapsack Ciphers

Crytographic Protocols and Applications

Primitive Roots

The Order of an Integer and Primitive Roots

Primitive Roots for Primes

The Existence of Primitive Roots

Index Arithmetic

Primality Testing Using Orders of Integers and Primitive Roots

Universal Exponents

Applications of Primitive Roots

Pseudorandom Numbers

The E1Gamal Cryptosystem

An Application to the Splicing of Telephone Cables

Quadratic Residues and Reciprocity

Quadratic Residues and Nonresidues

The Law of Quadratic Reciprocity

The Jacobi Symbol

Euler Pseudoprimes

Zero-Knowledge Proofs

Decimal Fractions and Continued Fractions

Decimal Fractions

Finite Continued Fractions

Infinite Continued Fractions

Periodic Continued Fractions

Factoring Using Continued Fractions

Some Nonlinear Diophantine Equations

Pythagorean Triples

Fermat's Last Theorem

Sums of Squares

Pell's Equations

Axioms for the Set of Integers

Binomial Coefficients

Using Maplereg; and Mathematica for Number Theory

Number Theory Web Links

Tables

Answers to odd-numbered exercises

Bibliography

Index of Biographies

Index

Table of Contents provided by Publisher. All Rights Reserved.