Solutions to diophantine equation $m^2-12mn-3m+2=0$

Question

I am trying to find all solutions to the relativly simple diophantine equation $m^2-12mn-3m+2=0$. I suspect that the only solutions are $n=0$, $m=1$ and $n=0$, $m=2$, but I am currently unable to show this. Any help is appreciated.

Henrik.

Answer 1

Hint: $m^2-12mn-3m=-2$ leaves limited options for $m$.