triangle112 09.04.2020 13:12 One can check that $(m, n)=(6, 3)$ is a solution. Assume $n \geq 4$, then $3^m \equiv 1 (.16)$ so $4|m$ and mod $5$ gives us $-1 \equiv 1 (.5)$, contradiction. So we have that $n \leq 3$ and the solution metioned above is the only one.