# Book:Alan Baker/A Concise Introduction to the Theory of Numbers

## Alan Baker: A Concise Introduction to the Theory of Numbers

Published $\text {1984}$, Cambridge University Press

ISBN 0-521-28654-9

### Contents

Preface
Introduction: Gauss and number theory
1 Divisibility
1 Foundations
2 Division algorithm
3 Greatest common divisor
4 Euclid's algorithm
5 Fundamental theorem
6 Properties of the primes
8 Exercises
2 Arithmetical functions
1 The function $\sqbrk x$
2 Multiplicative functions
3 Euler's (totient) function $\map \phi n$
4 The Möbius function $\map \mu n$
5 The functions $\map \tau n$ and $\map \sigma n$
6 Average orders
7 Perfect numbers
8 The Riemann zeta-function
10 Exercises
3 Congruences
1 Definitions
2 Chinese remainder theorem
3 The theorems of Fermat and Euler
4 Wilson's theorem
5 Lagrange's theorem
6 Primitive roots
7 Indices
9 Exercises
1 Legendre's symbol
2 Euler's criterion
3 Gauss' lemma
5 Jacobi's symbol
7 Exercises
1 Equivalence
2 Reduction
3 Representations by binary forms
4 Sums of two squares
5 Sums of four squares
7 Exercises
6 Diophantine approximation
1 Dirichlet's theorem
2 Continued fractions
3 Rational approximations
5 Liouville's theorem
6 Transcendental numbers
7 Minkowski's theorem
9 Exercises
1 Algebraic number fields
3 Units
4 Primes and factorization
5 Euclidean fields
6 The Gaussian field