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.