Quartic reciprocity

Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x⁴ ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x⁴ ≡ p (mod q) to that of x⁴ ≡ q (mod p).