3.62 On a grid paper of size $5 \times n$, it is completely covered with $1 \times 2$ rectangular cards, each card having a +1 and a -1 written in its two squares. It is known that in the resulting number table, the product of numbers in each row and each column is positive. Find all natural numbers $n$ that can form such a number table.
[Solution] First, when $n$ is odd, the total number of squares on the paper is odd, and it is of course impossible to cover them with $1 \times 2$ cards.

Second, when $n=4$, the cards can be laid out as shown in the right figure, clearly meeting the requirements of the problem. This indicates that when $4 \mid n$, a number table that meets the requirements can always be formed.

When $n$ is even but not a multiple of 4, $\frac{n}{2}$ is odd. Thus, the number of card blocks is odd, meaning that the number of -1s in the formed number table is odd. Since the table has an even number of columns ($n$ columns), there must be at least one column containing an odd number of -1s, making the product of the numbers in this column -1, which does not meet the requirements.

In summary, a $5 \times n$ number table that meets the requirements can be formed using the cards if and only if $4 \mid n$: