379. For which integers $m$ and $n$ does the equality

$$
(5+3 \sqrt{2})^{m}=(3+5 \sqrt{2})^{n}
$$

hold?
379. Answer: $m=n=0$. If $(5+3 \sqrt{2})^{m}=(3+5 \sqrt{2})^{n}$, then $(5-3 \sqrt{2})^{m}=(3-5 \sqrt{2})^{n}$, but this is impossible, since $0<5-3 \sqrt{2}<1$ and $3-5 \sqrt{2}<0$.