Determine all solutions $(m, n) \in \mathbf{N}^{2}$ of the equation:

$$
2^{m}-3^{n}=1
$$
$3^{n}$ is congruent to 1 or 3 modulo 8, depending on whether $n$ is even or odd, so $2^{m}=3^{n}+1$ must be congruent to 2 or 4 modulo 8, which is only satisfied for $m=1$ (thus $n=0$) and $m=2$ (thus $n=1$).