I am trying to solve the equation
$\frac{4}{9} = \big( \frac{1}{3} \big) ^n + \big( \frac{1}{3} \big) ^m $
with $n$ and $m$ both positive integers.
I type into Mathematica the following
In:= Solve[4/9 == 1/3^m + 1/3^n && m > 0 && n > 0, n, Integers]
which spits out "Solve::nsmet: This system cannot be solved with the methods available to Solve."
The solution to the problem is $n=1\:\&\:m=2$ or $n=2\:\&\:m=1$. How can I change my input to have Mathematica come up with this?