# Find all positive integers $a$ for which there exists some positive integer $b$ s.t. $(2^a-1)\mid(b^2+9)$

Find all positive integers $a$ for which there exists some positive integer $b$ s.t.

$(2^a-1)\mid(b^2+9)$

-
 Welcome to SE. It would be helpful if you explain what you tried so far and where you got stuck. This will help you get better answers to your question. – Ittay Weiss Nov 12 '12 at 6:46

First, handle the cases $a=1$ and $a=2$.
Then, for $a\gt2$, consider prime divisors congruent $3$ mod $4$ of $2^a-1$ and of $b^2+9$.