An Introduction to Number Theory
Harold Stark

MIT Press
ISBN 0-262-69-60-8



Table of contents

Chapter 1  An introduction to number theory
  1.1  An introduction to number theory
  1.2  Some elementary properties of divisibility
  
Chapter 2  The Euclidean algorithm and unique factorization
  2.1  The Euclidean algorithm
  2.2  The fundamenatal theorem of arithmetic
  2.3  Applications of the fundamental theorem
  2.4  Multiplicative functions
  2.5  Linear Diophantine equations
  
Chapter 3  Congruences
  3.1  Introduction
  3.2  Fundamental properties of congruences
  3.3  Linear congruence equations
  3.4  Reduced residue systems and Euler's phi function
  3.5  More on Euler's phi function
  3.6  Polynomial congruences
  3.7  Primitive roots
  
Chapter 4 Magic squares
  4.1  The uniform step method
  4.2  Filled and magic squares
  4.3  Diabolic and symmetric squares
  4.4  Historical comments
  
Chapter 5  Diophantine equations
  5.1  Introduction
  5.2  The use of congruences in solving Diophantine equations
  5.3  Pythagorean triples
  5.4  Fermat's method of descent

Chapter 6  Numbers, rational and irrational
  6.1  Rational numbers
  6.2  Irrational numbers
  6.3  Lieuville's theorem and transcendental numbers

Chapter 7  Continued fractions from a geometric viewpoint
  7.1  Introduction
  7.2  The continued fraction algorithm
  7.3  Computation of a(sub)n
  7.4  The best approximations
  7.5  A commentary of proof by picture
  7.6  Periodic continued fractions
  7.7  The Fermat-Pell equation and the continued fraction
       expansion of square roots

Chapter 8  Quadratic fields  
  8.1  Introduction
  8.2  Quadratic fields and quadratic integers
  8.3  Divisibility and factorization into primes
  8.4  Unique factorization and Euclidean domains
  8.5  Applications of quadratic fields to Diophantine equations
  8.6  Historical comments