This paper presents a proof of the fact that if the (circulant) von Neumann mean filter operator is defined on a square coordinate set with iem rows and iem columns, then it fails to be invertible only if either the integer 5 divides iem or the integer 6 divides iem. This result answers a question posed by P. Gader, who proved that the usual 3×3 mean filter operator is invertible if and only if 3 does not divide iem.