How find the $\inf\sqrt[r]{n_{1}n_{2}\cdots n_{r}}$ Let $r,n$ be given positive integers,and $n_{r}$ are positive integers, such
$$n_{1}+n_{2}+\cdots+n_{r}=n$$
find the
$$\inf\sqrt[r]{n_{1}n_{2}\cdots n_{r}}$$
I known use AM-GM $$n_{1}+n_{2}+\cdots+n_{r}\ge r\sqrt[r]{n_{1}n_{2}\cdots n_{r}}$$ so we have  find the sup is 
$$\dfrac{n}{r}?$$
and How to find the inf?

Let $x>y$, where $\{x,y\}\subset\mathbb N$.
Hence, since $xy\geq(x+1)(y-1)$, we get the minimum for $n_1=n_2=...=n_{r-1}=1$.
