AMC 12 2002b Problem 12

For how many integers $n$ is $\dfrac n{20-n}$ the square of an integer?

$\mathrm{(A)}\ 1 \mathrm{(B)}\ 2 \mathrm{(C)}\ 3 \mathrm{(D)}\ 4 \mathrm{(E)}\ 10$