Let $p$ be an odd prime of the form $p \equiv 1 \pmod 4$. Also let $r$ be a primitive root modulo $p$. Prove that $-r$ is also a primitive root of $p$.
We proved this as a lemma in the previous Exercise (6.4).11. We can interpret $p \equiv 1 \pmod 4$ as $\frac{p-1}{2}$ is even, using $p -1 = 4k \implies \frac{p-1}{2} = 2k$ for some integer $k$.