Legendre symbol

The Legendre symbol is a mathematical notation that provides a way to determine if a given integer is a quadratic residue modulo a prime number. Specifically, for an integer \( a \) and a prime \( p \), the Legendre symbol is denoted as: \[ \left( \frac{a}{p} \right) \] It is defined as follows: 1. If \( a \) is congruent to 0 modulo \( p \) (i.e.