3. It is known that for some positive coprime numbers $m$ and $n$, the numbers $m+2024 n$ and $n+2024 m$ have a common prime divisor $d>7$. Find the smallest possible value of the number $d$ under these conditions.
Answer: $d_{\min }=17$.

For example,

$$
\begin{aligned}
& m=16, n=1 \rightarrow 2024 m+n=2024 \cdot 16+1=32385=17 \cdot 1905 \\
& m+2024 n=16+2024=17 \cdot 120
\end{aligned}
$$