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Elementary Number Theory and Its Applications

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ISBN-10: 0321237072

ISBN-13: 9780321237071

Edition: 5th 2005 (Revised)

Authors: Kenneth H. Rosen

List price: $84.00
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Book details

List price: $84.00
Edition: 5th
Copyright year: 2005
Publisher: Addison-Wesley Longman, Incorporated
Publication date: 10/19/2004
Binding: Paperback
Pages: 744
Size: 7.25" wide x 9.25" long x 1.50" tall
Weight: 2.640
Language: English

What is Number Theory?
The Integers
Numbers and Sequences
Sums and Products
Mathematical Induction
The Fibonacci Numbers
Integer Representations and Operations
Representations of Integers
Computer Operations with Integers
Complexity of Integer Operations
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
Introduction to Congruences
Linear Congrences
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
Euler's Theorem
Multiplicative Functions
The Euler Phi-Function
The Sum and Number of Divisors
Perfect Numbers and Mersenne Primes
Mobius Inversion
Character Ciphers
Block and Stream Ciphers
Exponentiation Ciphers
Knapsack Ciphers
Cryptographic 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 Tests Using Orders of Integers and Primitive Roots
Universal Exponents
Applications of Primitive Roots and the Order of an Integer
Pseudorandom Numbers
The EIGamal Cryptosystem
An Application to the Splicing of Telephone Cables
Quadratic Residues
Quadratic Residues and nonresidues
The Law of Quadratic Reciprocity
The Jacobi Symbol
Euler Pseudoprimes
Zero-Knowledge Proofs
Decimal Fractions and Continued
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 Equation
The Gaussian Integers
Gaussian Primes
Unique Factorization of Gaussian Integers
Gaussian Integers and Sums of Squares