Abstract: | We show that if is a finite group, a conjugacy class of and , are the distinct elements in the multiset (here is the value of on any element of ), then This is a dual to a generalization of a theorem of Blichfeldt stating that if is a finite group, a generalized character and are the distinct values of , then We also observe that in Blichfeldt's congruence can be replaced, with a minor adjustment, by any rational value of . A similar change can be done to the first congruence above. |