IMO Shortlist 2010 problem N2


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June 23, 2013
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Find all pairs (m,n) of nonnegative integers for which m^2 + 2 \cdot 3^n = m\left(2^{n+1} - 1\right).

Proposed by Angelo Di Pasquale, Australia
Source: Međunarodna matematička olimpijada, shortlist 2010