Pearson eText -- Elementary Number Theory -- Access Card

About our author Kenneth H. Rosen received his BS in mathematics from the University of Michigan - Ann Arbor (1972) and his PhD in mathematics from MIT (1976). Before joining Bell Laboratories in 1982, he held positions at the University of Colorado - Boulder, The Ohio State University - Columbus, and the University of Maine - Orono, where he was an associate professor of mathematics. While working at AT&T Laboratories, he taught at Monmouth University, teaching courses in discrete mathematics, coding theory, and data security.  Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of Elementary Number Theory,  7th Edition and other books. 

The Integers

Numbers and Sequences
Diophantine Approximation
Sums and Products
Mathematical Induction
The Fibonacci Numbers
Divisibility


Integer Representations and Operations

Representations of Integers
Computer Operations with Integers
Complexity of Integer Operations


Greatest Common Divisors

Greatest Common Divisors and Their Properties
The Euclidean Algorithm
Linear Diophantine Equations


Prime Numbers

Prime Numbers
The Distribution of Primes
The Fundamental Theorem of Arithmetic
Factorization Methods and the Fermat Numbers


Congruences

Introduction to Congruences
Linear Congruences
The Chinese Remainder Theorem
Polynomial Congruences
Systems of Linear Congruences


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


Arithmetic Functions

The Euler Phi-Function
The Sum and Number of Divisors
Perfect Numbers and Mersenne Primes
Möbius Inversion
Partitions


Cryptography

Character Ciphers
Block and Stream Ciphers
Exponentiation Ciphers
Public Key Cryptography
Cryptographic Protocols and Applications


Primitive Roots

The Order of an Integer and Primitive Roots
Primitive Roots for Primes
The Existence of Primitive Roots
Discrete Logarithms and 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 Fractions

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


Nonlinear Diophantine Equations and Elliptic Curves

Pythagorean Triples
Fermat's Last Theorem
Sum of Squares
Pell's Equation
Congruent Numbers and Elliptic Curves
Elliptic Curves Modulo Primes
Applications of Elliptic Curves


The Gaussian Integers

Gaussian Integers and Gaussian Primes
Greatest Common Divisors and Unique Factorization
Gaussian Integers and Sums of Squares