1. Give an example of a positive integer divisible by 2020, in which the digits $0,1, \cdots, 9$ appear the same number of times.
1. The positive integer 98987676545431312020 is an example.
Notice that, $2020=4 \times 5 \times 101$.
Therefore, if a positive integer can be simultaneously divided by $4$, $5$, and 101, then it can be divided by 2020.

Since the example ends with 20, it can be simultaneously divided by 4 and 5.

Also, $\overline{a b a b}=101 \cdot \overline{a b}$, the example given is equal to the sum of integers of the form $\overline{a b a b} \cdot 10^{k}$, hence it can be divided by 101. [Note] Of course, there are other examples.