Division Theorem

For any integer a and positive integer n, there are unique integers q and r such that 0 $\leq$ r < n and a = qn + r

q (= $\lfloor$a/n$\rfloor$) is the quotient of the division

r (= a mod n) is the remainder

a = $\lfloor$a/n$\rfloor$n + (a mod n) or
a mod n = a - $\lfloor$a/n$\rfloor$n

If (a mod n) = (b mod n), then a $\equiv$ b (mod n)

Example

22 mod 5 = 2
-13 mod 5 = 2