General solution to the u(1) anomaly equations.

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Resumo

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.