Let $\displaystyle P(n)$ be the product of positive integers which are $\displaystyle \leq n$ and relatively prime to $\displaystyle n $. Prove that $\displaystyle \displaystyle P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \biggl(\frac{d!}{d^d} \biggr)^{\mu(n/d)} $