Table of Contents

Arithmetic of the Integers
Introduction - Where We Begin and Why
The Fundamental Laws
Divisibility
Prime Numbers
Computer Arithmetic and Complexity
Applications to a Set of Quadratics
Congruences
The Basics
Linear Congruences
Arithmetic Functions - Euler's Totient
The Chinese Remainder Theorem
Polynomial Congruences and Thue's Theorem
Cryptography and Factoring
Quadratic Polynomials
Primitive Roots
Order
Existence
Indices
Primality Testing and Cryptography
Quadratic Orders, Ideals and Units
Quadratic Residues
The Quadratic Reciprocity Law
The Jacobi and Kronecker Symbols
Quadratic Polynomials and Primes
Quadratic Residues and Primality Testing
Applications to Quadratic Orders
Continued Fractions
Finite Continued Fractions
Infinite Continued Fractions
Periodic Continued Fractions
Continued Fractions and Factoring
The Continued Fraction Algorithm
Diophantine Equations
Sums of Squares
The Equation x2 - Dy2 = n
Diophantine Equations of Higher Degree
Elliptic Curves, Factoring, and Primality
Applications: Algebraic Number Theory
Appendices
A. Set Theory
B. Primes = 9547 and Least Primitive Roots
C. Tables of Special Primes
D. Cunningham Factorizations
E. Pseudoprimes and Carmichael Numbers
F. Indices
G. Values of Some Arithmetic Functions
H. The ABC Conjecture
I. The Prime Number Theorem
Solutions to Odd-Numbered Exercises
Bibliography
List of Symbols
Index

Reviews

"The book's strengths lie in its currency, its many worked examples, historical footnotes, and references to the literature." - D.V. Feldman, University of New Hampshire, in CHOICE, April 1998 "a very useful addition to the many books on number theory with applications, and it is meant to be accessible to anyone from the novice to the research scientistprovides an excellent supplementary source of information for the reader, not least in the many biographical footnotes on the mathematicians involved in the subject matter, and there are also more than a thousand exercises and examples in the text. Besides various tables for results in computational number theory, the nine appendices cover material from set theory, which includes discussions on the axiom of choice and Zorn's Lemma, to the ABC conjecture." --P. Shiu, Zentralblatt MATH, Vol. 943