# Book:George Eyre Andrews/Number Theory

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## George Eyre Andrews: *Number Theory*

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

### Online Copies

### 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

- Chapter 1: BASIS REPRESENTATION
- Part II QUADRATIC CONGRUENCES
- Chapter 9: QUADRATIC RESIDUES
- 9-1 Euler's Criterion
- 9-2 The Legendre Symbol
- 9-3 The Quadratic Reciprocity Law
- 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 9: QUADRATIC RESIDUES
- Part III ADDITIVITY
- 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

- Chapter 11: SUMS OF SQUARES
- Part IV GEOMETRIC NUMBER THEORY
- Chapter 15 LATTICE POINTS
- 15-1 Gauss's Circle Problem
- 15-2 Dirichlet's Divisor Problem

- Chapter 15 LATTICE POINTS
- APPENDICES
- Appendix A
- Appendix B
- Appendix C
- Appendix D
- THE INTEGRAL TEST
- NOTES
- SUGGESTED READING
- BIBLIOGRAPHY
- HINTS AND ANSWERS TO SELECTED EXERCISES
- INDEX OF SYMBOLS
- INDEX