I am having trouble with this question. It comes from the 1997 APMO:
Find an integer in the range $100\leq n \leq1997$ such that $\frac{2^n+2}{n}$ is an integer.
When I first attempted this problem, I thought, maybe FLT (Fermat's Little Theorem) might apply to this. However, I soon found out that $n$ must be even, and the only even prime is 2, so FLT is useless. I really don't know what to do. Can someone please help?