Pearson eText -- Elementary Number Theory -- Access Card

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