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Let $p$ be a prime which is $5 \pmod {8}$. Let $r$ be an element of $\mathbb{Z}/p\mathbb{Z}^*$ of order $4$ and let $a$ be a quadratic residue modulo $p$. Prove that a solution of $x^{2}=a \pmod p$ is given by either $x=a^{(p+3)/8}$ or $x=ra^{(p+3)/8}$.

I tried showing $a^{(p+3)/4}=a \pmod p$, but I couldn't figure out how to proceed.

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