Cubic reciprocity

Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x³ ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of the main theorem, which states that if p and q are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence x³ ≡ p (mod q) is solvable if and only if x³ ≡ q (mod p) is solvable.