if "n" is even, then one may rewrite the "n" majorana fermions as "n"/2 dirac fermions. these have parity invariant mass terms, and so pauli–villars may be used to regulate the divergences and no parity anomaly arises. therefore, for even "n" there is no anomaly. moreover, as the contribution of 2n majorana fermions to the partition function is the square of the contribution of "n" fermions, the square of the contribution to the anomaly of "n" fermions must be equal to one. therefore, the anomalous phase may only be equal to a square root of one, in other words, plus or minus one. if it is equal to one, then there is no anomaly. therefore, the question is, when is there an ambiguity in the partition function of a factor of -1.