Let n be a positive integer. Define the function $f:\mathbb{Z}\to \mathbb{Z}/n\mathbb{Z}$ by $f(x) = [x]_n$. Prove that $f$ is a surjective homomorphism of rings.
So I know that in order to be a homomorphism of rings, we must show that $f(a + b) = f(a) + f(b)$ and $f(ac) = f(a) f(c)$.
So I know that we must show that the equivalence classes
$[a]_n + [b]_n = f(a + b)$ and the same for multiplication, but I am not quite sure where to start.