Quadratic residues

A quadratic residue is a number that can be expressed as the square of some other number, within a specific set of numbers called a modular system. For example, consider the numbers from 0 to 6, and pick a number like 2. If there's a number, say 3, such that 3 squared (3×3=9) gives us a number equivalent to 2 when divided by 7 (since 9 mod 7 = 2), then 2 is a quadratic residue modulo 7. Essentially, quadratic residues identify which numbers can be obtained by squaring numbers in a modular system, revealing patterns in how squares behave within that system.