elementary number theory - Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$

I'm trying to prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$. Can someone give a hint in the right direction for this?

Answer

Hint

Now, let $a=qb+r$ with $0 \leq r

$$2^a+1=2^a-2^r+2^r+1 $$

Show that $2^b-1 | 2^a-2^r$ and conclude that $2^b-1|2^r+1$. Now prove that this contradicts $0 \leq r