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Definition (Modular Arithmetic)
Let $a,b,n\in \mathbb{Z}$ with $n>0$. We say that two integers $a$ and $b$ are congruent mod $n$, and write $a \mod n= b\mod n$, if they have the same remainder after dividing by $n$. If $a=qn+r$ where $r$ is the remainder after dividing by $n$, then we'll often write $r=a\mod n$. There are lots of ways to denote this in the literature. We might say $r\equiv a\mod n$, $r=a\pmod n$, $a\mod n \equiv b \mod n$, and more.
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