I am looking for a proof of Gauss's generalization of Wilson's Theorem.
Let $S$ be the set of all the integers which are less than and mutually prime to $n (>4)$ (not of the form $p^\alpha$, $2p^\alpha$ for all odd $p$). Denote the elements of $S$ by $a_i$ $\forall i$ $\mid$ $1 \leq i \leq \phi(n)$ and $a_i<a_{i+1}$. Then show that,
$$\prod_{i=1}^{\phi(n)} a_i \equiv 1 \quad (\text{mod} n)$$
I have searched in Wikipedia but there is only the reference of Gauss's Arithmatica which I am unable to find as an e-book.
Any hint to the proof will be appreciated.