Gauss's lemma (number theory)

In number theory, Gauss's lemma is a result that relates to the quadratic residues modulo a prime. Specifically, it provides a criterion for determining whether a given integer is a quadratic residue modulo a prime number. The statement of Gauss's lemma can be formalized as follows: Let \( p \) be an odd prime, and let \( a \) be an integer that is not divisible by \( p \).