Past exam of the Probability, statistics and options II course of the University of Oxford / 2011 / C / C2 / a / i / Solution

A square residue modulo $p$ is a congruence class represented by $x^2$ for some integer $x$. For the final all-primes solvability statement, zero is included as a square. The Legendre symbol distinguishes the zero class from the nonzero square and nonsquare classes:When the term quadratic residue is reserved for nonzero classes, the zero case must be stated separately, as in this definition.