Let p be prime in Z with $\displaystyle p \equiv 1 \ (mod \ 4). $ Show that there is an integer $\displaystyle n \in Z$ with $\displaystyle n^2 \equiv -1 \ (mod \ p) $

Proof. Now I have p - 1 = 4k for some integers k. Then p = 4k - 1, pk = 4k^2 - k, so I have a square of something but with an extra k behind, how can I continue?

Thank you.