1. The sequence $\left\{x_{n}\right\}$ satisfies: $x_{n}=\frac{n}{n+2016}$, if $x_{2016}=x_{m} \cdot x_{n}$, then a solution for the positive integers $m, n$ is $\{m, n\}=$
$$
\begin{array}{l}
\frac{m}{m+2016} \cdot \frac{n}{n+2016}=\frac{1}{2} \Rightarrow 2 m n=(m+2016)(n+2016) \\
\Rightarrow m n-2016 m-2016 n=2016^{2} \Rightarrow(m-2016)(n-2016)=2 \cdot 2016^{2} \\
\Rightarrow m=3 \cdot 2016, n=2 \cdot 2016, \cdots \text{. So }\{m, n\}=\{6048,4032\} .
\end{array}
$$