General Solution to the U(1) Anomaly Equations

The anomaly cancellation equations for the U(1) gauge group can be written as a cubic equation in n−1 integer variables, where n is the number of Weyl fermions carrying the U(1) charge. We solve this Diophantine cubic equation by providing a parametrization of the charges in terms of n−2 integers, and prove that this is the most general solution.