Elementary Number Theory

ISBN-10: 0073051888

ISBN-13: 9780073051888

Edition: 6th 2007 (Revised)

Authors: David M. Burton
List price: $151.56
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Book details

List price: $151.56
Edition: 6th
Copyright year: 2007
Publisher: McGraw-Hill Higher Education
Binding: Hardcover
Pages: 448
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.584

Some Preliminary Considerations
Mathematical Induction
The Binomial Theorem
Early Number Theory
Divisibility Theory in the Integers
The Division Algorithm
The Greatest Common Divisor
The Euclidean Algorithm
The Diophantine Equation ax+by=c
Primes and Their Distribution
The Fundamental Theorem of Arithmetic
The Sieve of Eratosthenes
The Goldbach Conjecture
The Theory of Congruences
Carl Friedrich Gauss
Basic Properties of Congruence
Special Divisibility Tests
Linear Congruences
Fermat's Theorem
Pierre de Fermat
Fermat's Factorization Method
The Little Theorem
Wilson's Theorem
Number-Theoretic Functions
The Functions ��nd �&#227
The Mobius Inversion Formula
The Greatest Integer Function
An Application to the Calendar
Euler's Generalization of Fermat's Theorem
Leonhard Euler
Euler's Phi-Function
Euler's Theorem
Some Properties of the Phi-Function
An Application to Cryptography
Primitive Roots and Indices
The Order of an Integer Modulo n
Primitive Roots for Primes
Composite Numbers Having Prime Roots
The Theory of Indices
The Quadratic Reciprocity Law
Euler's Criterion
The Legendre Symbol and Its Properties
Quadratic Reciprocity
Quadratic Congruences with Composite Moduli
Perfect Numbers
The Search for Perfect Numbers
Mersenne Primes
Fermat Numbers
The Fermat Conjecture
Pythagorean Triples
The Famous ��Last Theorem��
Representation of Integers as Sums of Squares
Joseph Louis Lagrange
Sums of Two Squares
Sums of More than Two Squares
Fibonacci Numbers
The Fibonacci Sequence
Certain Identities Involving Fibonacci Numbers
Continued Fractions
Srinivasa Ramanujan
Finite Continued Fractions
Infinite Continued Fractions
Pell's Equation
Some Twentieth-Century Developments
Hardy, Dickson, and Erdos
Primality Testing and Factorization
An Application to Factoring: Remote Coin-Flipping
The Prime Number Theorem
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