Past exam of the options II for mathematics and philosophy course of the University of Oxford / 2013 / C2 / a / i / Solution

For an odd prime $p$, the Legendre symbol is zero if $p\mid a$, one if $a$ is a nonzero quadratic residue modulo $p$, and minus one if it is a quadratic nonresidue. ThusIt depends only on the congruence class of $a$ modulo $p$.