reciprocity law

If there exists a rational integer x such that, when n, p, and q are positive integers, x^n congruent q (mod p), then q is the n-adic residue of p, i.e., q is an n-adic residue of p iff x^n congruent q (mod p) is solvable for x. Reciprocity theorems relate statements of the form "p is an n-adic residue of q" with reciprocal statements of the form "q is an n-adic residue of p."

Artin's reciprocity theorem | biquadratic reciprocity theorem | class field theory | class number | cubic reciprocity theorem | Langlands program | Langlands reciprocity | octic reciprocity theorem | quadratic reciprocity theorem