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 \(a\equiv b\bmod{n}\) 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 \(1 + 5^2 + 5^3 \equiv 151\bmod{3}\).