Let $p$ be a prime number such that $p \equiv 2 \pmod 3$. Prove that the function $f : \mathbb{Z}_p \to \mathbb{Z}_p$, with $f(x) = x^3$ is bijective.
Besides the fact that $p = 3k+2$, for some integer $k$, I haven't figured out anything meaningful yet.
Thank you in advance!
