$2^n= n^2$ is true for 2 integers:
$n=2$ --> $2^2=2^2=4$;
$n=4$ --> $4^2=2^4=16$.

Well, $2^2=2^2=4$ is obvious choices, then after trial and error you'll get $4^2=2^4=16$ as well. But how do we know that there are no more such numbers? You can notice that when $n$ is more than 4 then $2^n$ is always more than $n^2$ so $n$ cannot be more than 4. $n$ cannot be negative either as in this case $2^n$ won't be an integer whereas $n^2$ will be.

Answer: C.