QED at a finite chemical potential

We consider multi-flavor QED on a finite lattice at a finite chemical potential and show that the partition function only depends on the variables, $(\frac{\mu_i}{q_i} -\frac{\mu_1}{q_1})$, for $i=2,...$, where $q_i$, $i=1...$ are integer valued charges of the various flavors and $\mu_i$, $i=1...$ are the dimensional chemical potentials of the various flavors.