Prove that $f(x)=(x^2-2)(x^2-3)(x^2-6)$ has a root in $\mathbb{F}_p$ for every $p$ prime number
Prove that $z^2 \equiv ab\pmod p$ is solvable if and only if both or neither of $x^2 \equiv a \pmod p$, $x^2 \equiv b \pmod p$ are solvable.