Octic reciprocity

Octic reciprocity is a concept in number theory, particularly in the field of algebraic number theory, which extends the idea of reciprocity laws for quadratic residues (the classical quadratic reciprocity) to higher powers. While the classic quadratic reciprocity law, proven by Carl Friedrich Gauss, deals with the solvability of certain congruences involving squares (i.e., second powers), octic reciprocity focuses on eighth powers.