# Book:George E. Andrews/Number Theory

## Contents

## George E. Andrews: *Number Theory*

Published $1971$, **Dover Publications, Inc.**

- ISBN 0-486-68252-8.

### Subject Matter

### Contents

**Preface**

**Part I: Multiplicativity - Divisibility**

- Chapter 1: Basis Representation
- Chapter 2: The Fundamental Theorem of Arithmetic
- Chapter 3: Combinatorial and Computational Number Theory
- Chapter 4: Fundamentals of Congruences
- Chapter 5: Solving Congruences
- Chapter 6: Arithmetic Functions
- Chapter 7: Primitive Roots
- Chapter 8: Prime Numbers

**Part II: Quadratic Congruences**

- Chapter 9: Quadratic Residues
- Chapter 10: Distribution of Quadratic Residues

**Part III: Additivity**

- Chapter 11: Sums of Squares
- Chapter 12: Elementary Partition Theory
- Chapter 13: Partition Generating Functions
- Chapter 14: Partition Identities

**Part IV: Geometric Number Theory**

- Chapter 15: Lattice Points

**Appendices***Appendix A*: A proof that $\displaystyle \lim_{n \mathop \to \infty} \map p n^{1/n} = 1$*Appendix B*: Infinite Series and Products*Appendix C*: Double Series*Appendix D*: The Integral Test

- Notes
- Suggested Reading
- Bibliography
- Hints and Answers to Selected Exercises
- Index of Symbols
- Index

## Errata

### Solution to Difference between Odd Squares is Divisible by 8

Chapter $2$: The Fundamental Theorem of Arithmetic:

*Since $a$ and $b$ are odd integers, $a = 2 r + 1$, and $b = 2 s + 1$. Thus**$a^2 - b^2 = \paren {4 r^2 + 4 r + 1} - \paren {4 s^2 + 4 s + 1} = 4 \paren {r - s} \paren {r - s + 1}$.*

*Now if $r - s$ is even, then $r - s = 2 m$ and $a^2 - b^2 = 8 m \paren {2 m + 1}$; if $r - s$ is odd, then $r - s = 2 n + 1$ and $a^2 - b^2 = 8 \paren {2 n + 1} \paren {n + 1}$. Thus in any case $a^2 - b^2$ is divisible by $8$ if $a$ and $b$ are odd integers.*