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Elementary Number Theory and Its Applications

Elementary Number Theory and Its Applications - 3rd edition

Elementary Number Theory and Its Applications - 3rd edition

ISBN13: 9780201578898

ISBN10: 0201578891

Elementary Number Theory and Its Applications by Kenneth H. Rosen - ISBN 9780201578898
Edition: 3RD 93
Copyright: 1993
Publisher: Addison-Wesley Longman, Inc.
International: No
Elementary Number Theory and Its Applications by Kenneth H. Rosen - ISBN 9780201578898

ISBN13: 9780201578898

ISBN10: 0201578891

Edition: 3RD 93

Other Editions of Elementary Number Theory and Its Applications

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This third edition preserves the strengths of the previous editions while enhancing the text's teachability, flexibility, and richness. It incorporates feedback from many of the more than 200 schools where this text has been used. The blending of classical theory with modern applications has always been a hallmark of the text, and this new edition builds on this strength with new examples and additional applications. Many new exercises, including more routine exercises, along with many new intermediate, challenging, and extremely challenging exercises are provided. Challenging and extremely challenging exercises are clearly marked in the text. New to this edition are answers or solutions to all odd-numbered exercises at the end of the text.


  • Sections on check digits and zero knowledge proofs are included.
  • Coverage of elementary factoring methods, including the Pollard p-1 method and the Pollard rho method, were expanded.
  • Information on recent developments in number theory, such as new big prime numbers and factorizations of large integers, was updated.
  • Ten additional biographies of mathematicians bring the text's total to more than 25.
  • Computations and Explorations allow students to use computer programs to discover new ideas.
  • Applications are integrated with text material.
  • Exercises range from routine to challenging.
  • Coverage of number theory and cryptology is integrated and comprehensive.
  • Excellent computer science applications include hashing functions, arithmetic with large integers, pseudo-primes, and probabalistic primality testing.

Table of Contents

Table of Contents

Chapter 1: Introduction

Chapter 2: The Integers

Basic Properties
Summations and Products
Mathematical Induction
Binomial Coefficients
Representations of Integers
Computer Operations with Integers
Complexity of Integer Operations
Prime Numbers

Chapter 3: Greatest Common Divisors and Prime Factorization

Greatest Common Divisors
The Euclidean Algorithm
The Fundamental Theorem of Arithmetic
The Fermat Numbers and Factorization Methods
Linear Diophantine Equations

Chapter 4: Congruencies

Introduction to Congruencies
Linear Congruencies
The Chinese Remainder Theorem
Systems of Linear Congruencies
Factoring Using the Pollard rho Method

Chapter 5: Applications of Congruencies

Divisibility Tests
The Perpetual Calendar
Round-Robin Tournaments
Computer File Storage and Hashing Functions
Check Digits

Chapter 6: Some Special Congruencies

Wilson's Theorem and Fermat's Little Theorem
Euler's Theorem

Chapter 7: Multiplicative Functions

Euler's Phi-Function
The Sum and Number of Divisors
Perfect Numbers and Mersenne Primes

Chapter 8: Cryptology

Character Ciphers
Block Ciphers
Exponentiation Ciphers
Public-Key Cryptography
Knapsack Ciphers
Some Applications to Computer Science

Chapter 9: Primitive Roots

The Order of an Integer and Primitive Roots
Primitive Roots for Primes
Existence of Primitive Roots
Index Arithmetic
Primality Testing Using Primitive Roots
Universal Exponents
Pseudo-Random Numbers
An Application to the Splicing of Telephone Cables

Chapter 10: Quadratic Residues and Reciprocity

Quadratic Residues and Nonresidues
Quadratic Reciprocity
The Jacobi Symbol
Euler Pseudoprimes
Zero-Knowledge Proofs

Chapter 11: Decimal Fractions and Continued Fractions

Decimal Fractions
Finite Continued Fractions
Infinite Continued Fractions
Periodic Continued Fractions
Factoring Using Continued Fractions

Chapter 12: Some Nonlinear Diophantine Equations

Pythagorean Triples
Fermat's Last Theorem
Sums of Squares
Pell's Equations


Other Editions of Elementary Number Theory and Its Applications

Elementary Number Theory and Its Applications by Kenneth H. Rosen - ISBN 9780201870732