58. 09. For any natural number $k$, we call a rectangle of size $1 \times k$ a "strip". Try to determine for which natural numbers $n$, a rectangle of size $1995 \times n$ can be divided into distinct "strips"?

58. 09. Clearly, the sides of the "strips" are parallel to the sides of the given rectangle. Let's assume the side lengths of the rectangle are in centimeters. We will discuss the following two cases.
(1) $n<1995$. In this case, the maximum length of the "strips" that can be divided is $1995 \mathrm{~cm}$. However, the area that can be covered by "strips" of different sizes does not exceed
$$
1+2+\cdots+1995=\frac{1}{2} \times 1995 \times 1996\left(\mathrm{~cm}^{2}\right),
$$

while the area of the given rectangle is $1995 n \mathrm{~cm}^{2}$. Therefore,
$$
\frac{1}{2} \times 1995 \times 1996 \geqslant 1995 n,
$$

which implies $n \leqslant \frac{1}{2} \times 1996=998$.
For $\boldsymbol{n} \leqslant 998$, we can provide an appropriate method to divide the $1995 \times n$ rectangle into different "strips". For example, first divide the $1995 \times n$ rectangle into $n$ strips, each of length 1995, leaving one strip as is, divide the second strip into lengths of 1 and 1994, divide the third strip into lengths of 2 and 1993, and so on.
(2) $n \geqslant 1995$. In this case, the maximum length of the "strips" that can be divided is $n \mathrm{~cm}$. The area that can be covered by "strips" of different lengths, not exceeding $n$, does not exceed
$1+2+\cdots+n=\frac{1}{2} n(n+1)$,
so, $\frac{1}{2} n(n+1) \geqslant 1995 n$,
which implies $n \geqslant 3991$.

We can similarly provide a method for dividing the rectangle in this case.
In summary, we know that $n \leqslant 998$ or $n \geqslant 3991$.