Find all positive integers n such that $2^2 + 2^5+ 2^n$ is a perfect square. Find all positive integers n such that $2^2 + 2^5 + 2^n$ is a perfect square. Explain your answer.

We have:
$$2^n+36=m^2$$
$$2^n=(m-6)(m+6)$$
Both $m-6$ and $m+6$ must be powers of $2$ (and note that they differ by $12$). Can you continue?
