Legendre symbol

Let $𝑝$ be an odd prime, $𝑎$ be an integer, and $Q$ be the set of quadratic residues mod $𝑝$ . The Legendre symbol is defined as num

(𝑎 𝑝) = ⎧ { {⎨ { {⎩ 0 𝑎 \equiv 𝑝 0 - 1 [𝑎] \notin Q + 1 [𝑎] \in Q ∖ {[0]}