[Solution] Take a set of 996 integers
$$M=\left\{a_{i} \mid a_{i}=0,1,2, \cdots, 995\right\} .$$

Then for all $i \neq j, \quad i, j=0,1,2, \cdots, 995$.
\begin{array}{l} a_{i}+a_{j} \leqslant 995+994=1989, \\ 0996$, so there exist at least two different numbers $a_{i}, a_{j}$, such that $a_{i}=-a_{j}$, thus we have
1991 \mid\left(a_{i}+a_{j}\right) \text {. }
$$$$