Solving for m yields m=4/3 + 1/3((16n-12)/(3n^2 - 4n)).
So F=(16n-12)/(3n^2-4n) must be an integer of the form 3k-1 with both m and n not zero. Only integer values of n from -4 to 6 need be considered since any others make F less than 1 in absolute value. I found only n=2 and m=3 works.
unique solution?
