Solution (source code)

= Solution
{c}

The <Legendre symbol> is
$$
\boxed{\left(\frac ap\right)=\begin{cases}0,&p\mid a,\\1,&a\text{ is a nonzero square modulo }p,\\-1,&a\text{ is not a square modulo }p.\end{cases}}
$$
It depends only on the residue class of $a$ modulo the odd prime $p$.