Lecture 6 - Introduction to modular arithmetic.

In this video, we introduce the concept of modular arithmetic.

1. Congruence modulo n - Let $a,b\in \mathbb{Z}$. Then $a\equiv bmodn$ if $n$ divides $b-a$ or in other words $a+nk=b$ for some integer $k$.

2. Congruence modulo $n$ lets us take an equation and reduce modulo $n$. For example, the equation $1+5^2+5^3=151$ becomes $1+5^2+5^3\equiv 151mod3$.