337. A sheet of paper was torn into 5 pieces, some of these pieces were torn into 5 parts, some of these new parts were torn again into 5 parts, and so on. Can this method result in 1994 pieces of paper? What about 1997?
$\triangle$ Each time a sheet or a piece of paper is torn into 5 parts, the total number of pieces increases by 4. Therefore, the number of paper pieces at each step can only be of the form $4k+1 (k \in N)$. This expression is the invariant.

Since $1994 \neq 4k+1 (k \in N)$, it is impossible to obtain 1994 pieces, while $1997 = 4k+1$ when $k=499$, so it is possible to obtain 1997 pieces.

Answer: 1994 pieces cannot be obtained, 1997 can.