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

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

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    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.2012-11-12
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    This is an old question from an IMO Shortlist (1998?).2013-09-03

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