IMO Shortlist 2010 problem N2
Dodao/la:
arhiva23. lipnja 2013. Find all pairs
![(m,n)](/media/m/4/2/0/4202026f5dcd727e559bf78936cde057.png)
of nonnegative integers for which
![m^2 + 2 \cdot 3^n = m\left(2^{n+1} - 1\right).](/media/m/5/b/a/5ba02be75d6e65cec4e42deb2cdca1ab.png)
Proposed by Angelo Di Pasquale, Australia
%V0
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
Izvor: Međunarodna matematička olimpijada, shortlist 2010