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Question: Is $7^{50}$ a Quadratic Residue mod 101? Attempt: Theorem 9.1 states that the number $a$ is a Quadratic Residue if and only if $a^{\frac{p-1}{2}} \equiv 1$ (mod $p)$. Suppose $p=101,a^{\frac{p-1}{2}} =50,$ and $ a=7$ We need to find out whether or not the remainder will be one if ...