Im am searching for the following problem, but I have no idea how to start with it. Can someone help me with this?
Let $p$ be a prime congruent to $3 \mod 4$ and let $f \in \mathbb{F}_p[x]$ be such that $f(-x) = -f(x)$ for all $x \in \mathbb{F}_p$. Show that the equation $y^2 = f(x)$ has precisely $p$ solutions $(x, y)$ with $x, y \in \mathbb{F}_p$.