Question 24
Find all pairs $(m, n)$ of nonnegative integers for which
$$
m^{2}+2 \cdot 3^{n}=m\left(2^{n+1}-1\right)
$$
$$
m^{2}+2 \cdot 3^{n}=m\left(2^{n+1}-1\right)
$$
IMO 2010 — Complete Shortlist Question 24
IMO Shortlist · IMO 2010 — Complete Shortlist