. Let $n = p_0^{e_0}p_0^{e_0} \cdots p_s^{e_s}$ be the factorization of $n \in \mathbb{N}$ into powers of distinct primes $p_i,\ 0\leq i \leq s.$ In the case that the orders of $q$ modulo all these prime powers $p_i^{e_i}$ are pairwise coprime