RSA encoding function is bijection

Question

I need help with proving that function $E: \mathbb{Z_n} \to \mathbb{Z_n}, \ E(s) = s^e (\mbox{mod n}), \ \ gcd(e, \phi(n))=1$ is bijection.

I need to show that:

a) $E(x) = E(y) \Rightarrow x = y $

b) $ \forall y \in \mathbb{Z_n} \ \ \ \exists x \in \mathbb{Z_n} \ \ \ E(x) = y $

So in a) I have $E(x) = E(y) \Rightarrow x^e = y^e (\mbox{mod n}) \ \ \Rightarrow x^e - y^e = 0 (\mbox{mod n})$. What now?

Answer 1

Take $n=12$, $\phi(n)=4, e=3$, $6^3=0$ mod $12$