Legendre Symbol

The Legendre Symbol states that taken two numbers $a,p$, then $a$ is a quadratic residue of $p$ if $a$ is congruent to a perfect square modulo $p$. The function states that:

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