Let $p$ be an odd prime with primitive root $r$. Let $\mathbb{a}$ be an integer with $gcd(\mathbb{a},p) =1$ and $ind_{r} (\mathbb{a})$ denote the index of $\mathbb{a}$ relative to $r$.
Show that $\mathbb{a}$ is a quadratic residue modulo $p$ iff $ind_{r} (\mathbb{a})$ is even.
Could anyone give me a hint for solving this, please?
For the index of an integer w.r.t quadratic residue, Please follow the link.