[[Number theory MOC]]
# Quadratic residue

A **quadratic residue** in [[Modular arithmetic|$\mathbb Z_p$]] is an element which is the square of another, #m/def/num 
i.e. the set of all quadratic residues is
$$
\begin{align*}
\mathcal{Q} = \{ x^2 : x \in \mathbb{Z}_{p} \}
\end{align*}
$$
See also [[Legendre symbol]].


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