By which natural numbers can the fraction $\frac{3 m-n}{5 n+2 m}$ be reduced, given that it is reducible and that the numbers $m$ and $n$ are coprime.
If $3 m-n$ and $5 n+2 m$ are divisible by $d$, then the numbers $17 m=5(3 m-n)+5 n+2 m$ and $17 n=3(5 n+2 m)-2(3 m-n)$ are also divisible by $d$. But $\operatorname{HOK}(17 m, 17 n)=17$. Therefore, $d=17$. This is possible, for example, when $m=1, n=3$ (or when $m=$ $6, n=1)$.

## Answer

Divisible by 17.