For a given integer $n>0$, can we construct a ring $(R,+,\times)$ such that the subset $R^\times$ formed by the invertible elements of $R$ is a group of order $n$ under law $\times$, and how ?
When $n=p^k-1$ for some prime $p$ and integer $k$, we can use the finite field $\mathbb F_{p^k}$ for $R$. But what about other $n$?
