The Legendre Symbol is a mathematical notation used in number theory to determine whether a given integer is a quadratic residue modulo a prime number. It is denoted as (a/p), where a is an integer and p is an odd prime. If (a/p) = 1, it means a is a quadratic residue modulo p; if (a/p) = -1, it is not; and if (a/p) = 0, a is divisible by p. The Legendre Symbol plays a crucial role in various areas of mathematics, including quadratic reciprocity and cryptography. It helps in solving equations of the form x^2 \equiv a \mod p and is essential for understanding the properties of prime numbers. This symbol simplifies the process of determining the solvability of quadratic equations in modular arithmetic.