# Number of ordered pairs

Number Theory Level 5

$m^{2}+2(3^{n})=m(2^{n+1}-1)$ $$m,n$$ are positive integers . $$(m_{1},n_{1})......,(m_{ω},n_{ω})$$ be the solutions to the above equation. Find $$ω+\sum_{i=1}^{ω}m_{i}+n_{i}$$.

Problem is original.

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