Question 2
Prove that for every positive integer $n$, there exists a positive integer $k$ such that each of the numbers $k, k^2, \dots, k^n$ has at least one 2022 block in its decimal representation.
(For example, the numbers $4202213$ and $544202212022$ have at least one 2022 block in their decimal representation.)
(For example, the numbers $4202213$ and $544202212022$ have at least one 2022 block in their decimal representation.)