Find all positive integers $m$ and $n$ such that $$m^2+2\cdot 3^n=m(2^{n+1}-1).$$
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Fist thought: Take modulo $m$ on both sides, and you see that $2 \times 3^n \equiv 0 \mod{m}$. This should filter out quite much ... – Matti P. Apr 23 '19 at 09:15
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I mean I got that, and I know that m is either a power of 3 or 2 multiplied by a power of 3 but I am not sure of how to continue from there. – FC Barcelona Apr 23 '19 at 09:27