## TOC

- Introduction
- Complete and Reduced Residue Systems
- Euler's Totient Function
- Calculating the Totient Function by Hand

## Introduction

Today we're going to delve into a little bit of number theory.

In number theory, we are usually dealing with modular arithmetic - expressions of the form:

or

The mod indicates we're doing modular arithmetic, which is (formally) an algebraic system called a ring, which consists of the integers 0 through m.

An analogy to modular arithmetic is the way that the sine and cosine function "wrap around," and