# Book:George Eyre Andrews/Number Theory

## George Eyre Andrews: Number Theory

Published $1971$, W.B. Saunders Company.

### Contents

Part I MULTIPLICATIVITY--DIVISIBILITY
Chapter 1: BASIS REPRESENTATION
1-1 Principle of Mathematical Induction
1-2 The Basis Representation Theorem
Chapter 2: THE FUNDAMENTAL THEOREM OF ARITHMETIC
2-1 Euclid's Division Lemma
2-2 Divisibility
2-3 The Linear Diophantine Equation
2-4 The Fundamental Theorem of Arithmetic
Chapter 3: COMBINATORIAL AND COMPUTATIONAL NUMBER THEORY
3-1 Permutations and Combinations
3-2 Fermat's Little Theorem
3-3 Wilson's Theorem
3-4 Generating Functions
3-5 The Use of Computers in Number Theory
Chapter 4: FUNDAMENTALS OF CONGRUENCES
4-1 Basic Properties of Congruences
4-2 Residue Systems
4-3 Riffling
Chapter 5: SOLVING CONGRUENCES
5-1 Linear Congruences
5-2 The Theorems of Fermat and Wilson Revisited
5-3 The Chinese Remainder Theorem
5-4 Polynomial Congruences
Chapter 6: ARITHMETIC FUNCTIONS
6-1 Combinatorial Study of $\phi(n)$
6-2 Formulae for $d(n)$ and $\sigma(n)$
6-3 Multiplicative Arithmetic Functions
6-4 The Möbius Inversion Formula
Chapter 7: PRIMITIVE ROOTS
7-1 Properties of Reduced Residue Systems
7-2 Primitive Roots modulo $p$
Chapter 8: PRIME NUMBERS
8-1 Elementary Properties of $\pi(x)$
8-2 Tchebychev's Theorem
8-3 Some Unsolved Problems About Primes
9-1 Euler's Criterion
9-2 The Legendre Symbol
9-4 Applications of the Quadratic Reciprocity Law
Chapter 10: DISTRIBUTION OF QUADRATIC RESIDUES
10-1 Consecutive Residues and Nonresidues
10-2 Consecutive Triples of Quadratic Residues
Chapter 11: SUMS OF SQUARES
11-1 Sums of Two Squares
11-2 Sums of Four Squares
Chapter 12: ELEMENTARY PARTITION THEORY
12-1 Introduciton
12-2 Graphical Representation
12-3 Euler's Partition Theorem
12-4 Searching for Partition Identities
Chapter 13 GENERATING FUNCTIONS
13-1 Infinite Products As Generating Functions
13-2 Identities Between Infinite Series and Products
Chapter 14 PARTITION IDENTITIES
14-1 History and Introduction
14-2 Euler's Pentagonal Number Theorem
14-3 The Rogers-Ramanujan Identities
14-4 Series and Product Identities
14-5 Schur's Theorem
Part IV GEOMETRIC NUMBER THEORY
Chapter 15 LATTICE POINTS
15-1 Gauss's Circle Problem
15-2 Dirichlet's Divisor Problem
APPENDICES
Appendix A
Appendix B
Appendix C
Appendix D
THE INTEGRAL TEST
NOTES