Modular Arithmetic

Why

We want to count in circles.¹

Definition

Let $n \in \Z $ with $n > 1$ and take $a, b \in \Z $. The integers $a$ and $b$ are congruent modulo $n$ (or with respect to the modulus $n$) if $n$ is a divisor of their difference.²

1. Future editions will expand. ↩︎
2. Future editions will expand, and may need a sheet on congruence relations. ↩︎