Let $a,b,$ be positive integers and $a>b>2$. Prove that $\frac{2^a+1}{2^b-1}$ is never an integer
Source: Singapore Junior Math Olympiad 2013 2nd Round p4 SMO
Tags: Integer, number theory
Let $a,b,$ be positive integers and $a>b>2$. Prove that $\frac{2^a+1}{2^b-1}$ is never an integer