In mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials with integer coefficients. Recall that first reciprocity law, quadratic reciprocity, determines when an irreducible polynomial splits into linear terms when reduced mod . That is, it determines which prime numbers the relation holds. For a general reciprocity lawpg 3, it is defined as the rule determining which primes the polynomial splits into linear factors, denoted .