aureum theorema | Gauss's reciprocity theorem | golden theorem | Legendre's quadratic reciprocity law | quadratic reciprocity law

The quadratic reciprocity theorem is a theorem that tells whether a quadratic equation modulo a prime has a solution.

If p and q are distinct odd primes, then the quadratic reciprocity theorem states that the congruences x^2 congruent q (mod p) x^2 congruent p (mod q) are both solvable or both unsolvable unless both p and q leave the remainder 3 when divided by 4 (in which case one of the congruences is solvable and the other is not).

genus theorem | Jacobi symbol | Kronecker symbol | Legendre symbol | quadratic | quadratic residue | reciprocity theorem

college level