If $p$ is a prime in $\mathbb{Z}$ and $(p)$ is a prime ideal in $\mathbb{Z}[i]$, then $x^2 \equiv -1\pmod{p}$ has no solution in $\mathbb{Z}[i]$

Question

I can't find the proof for this. I know that $\mathbb{Z}[i]/(p)$ is an integral domain, so I tried to assume that there is a solution for $x \in \mathbb{Z}[i]$ and reach a contradiction of that fact, or the fact that $p$ is prime, but I wasn't able to do it. Can you help me? Thanks!