Natural numbers $m$ and $n$ are such that $m>n$, $m$ does not divide $n$, and the remainder of $m$ divided by $n$ is the same as the remainder of $m+n$ divided by $m-n$.

Find the ratio $m: n$.
Let $m=n q+r, 0<r<n$, then $q>1$. Therefore, $m / n>2$, and $\frac{m+n}{m-n}=1+\frac{2}{\frac{m}{n}-1}$. Since $m>n$, we have $m+r>(m-n)+r$, thus $m+n=2(m-n)+r$, which means $n q+n+r=2(n q+r-n)+r, (q-3) n+2 r=0$. From this, $q=2, n=2 r, m=5 r$.

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