16. Let $m$ and $n$ be positive integers satisfying
$$
m n^{2}+876=4 m n+217 n \text {. }
$$

Find the sum of all possible values of $m$.
16. Answer: 93 .
Rearranging, we have
$$
m n^{2}-217 n=4 m n-876 \Rightarrow n=\frac{4 m n-876}{m n-217}=4-\frac{8}{m n-217} .
$$

Then $(m n-217) 8$. It follows that $m n-217= \pm 1, \pm 2, \pm 4, \pm 8$.
So $m n=218,216,219,215,221,213,225,209$, and $n=-4,12,0,8,2,6,3,5$ respectively.
Note that $m=\frac{m n}{n}$ is a positive integer. Then $m=\frac{216}{12}=18$ or $m=\frac{225}{3}=75$.