TITLE: Find all positive integers satisfying $\frac{2^n+1}{n^2} =k $
QUESTION [5 upvotes]: Find all positive integers satisfying 
$$\frac{2^n+1}{n^2} =k $$
where $k$ is a integer. 
I can't just come up with a solution.

REPLY [2 votes]: This problem is extremely famous in world of Olympiad mathematics(It appeared in IMO 1990 , Problem-3) . This problem is famous, because it is also very easily solvable by use of Lifting the exponent lemma If you don't know about this lemma yet, then read this article, you will never regret. 
Otherwise, see this.