3: In the sequence of natural numbers $1,2,3, \cdots, n, \cdots$, the sum of numbers from the $m$-th $(m$ $<n$ ) to the $n$-th number is 1997. Then $m$ equals $\mathrm{f}$
3. 998 .
$(m+n)(n-m+1)=2 \cdot 1997, 1997$ is a prime number.
(1) $\left\{\begin{array}{l}m+n=1997, \\ n-m+1=2 ;\end{array}\right.$
(2) $\left\{\begin{array}{l}m+n=2 \cdot 1997, \\ n-m+1=1\end{array}\right.$
| (1), $n=999, m=998$.
| (2), $m=n=1997$ (discard).