  Costa et al. [Phys. Rev. Lett. 123, 151601 (2019)] recently gave a general
solution to the anomaly equations for $n$ charges in a $U(1)$ gauge theory.
`Primitive' solutions of chiral fermion charges were parameterised and it was
shown how operations performed upon them (concatenation with other primitive
solutions and with vector-like solutions) yield the general solution. We show
that the ingenious methods used there have a simple geometric interpretation,
corresponding to elementary constructions in number theory. Viewing them in
this context allows the fully general solution to be written down directly,
without the need for further operations. Our geometric method also allows us to
show that the only operation Costa et al. require is permutation. It also gives
a variety of other, qualitatively similar, parameterisations of the general
solution, as well as a qualitatively different (and arguably simpler) form of
the general solution for $n$ even.
