The set of k-units modulo n

Let R be a ring with identity, U(R) the group of units of R and k a positive integer. We say that a ∈ U(R) is k-unit if ak = 1. Particularly, if the ring R is Zn, for a positive integer n, we will say that a is a k-unit modulo n. We denote with Uk(n) the set of k-units modulo n. By duk(n) we represe...