Legendre Symbol

A Multiplicative Function comprised of $a,p\in \mathbb{Z}$

$$(\frac{a}{p})=\{\begin{array}{ll}1& \text{ if a is a quadratic residue modulo p and a}\not\equiv \mathrm{mod}p\\ -1& \text{ if a is a quadratic nonresidue modulo p}\\ 0& \text{ if a }\equiv 0\mathrm{mod}p\end{array}$$