Quadratic reciprocity

Quadratic reciprocity is a fundamental concept in number theory that reveals a surprising relationship between whether two different numbers are squares modulo each other. Specifically, it helps determine if one number is a quadratic residue (a perfect square) when divided by another, and vice versa. Essentially, it connects the solvability of certain equations in modular arithmetic in a symmetric way. This principle simplifies understanding complex relationships between primes and provides a powerful tool for solving equations involving square roots in modular systems.