8.1. Is the number $10^{2021}-2021$ divisible by 9?
Answer: No.

Solution. Let's write the number as $10^{2021}-1-2020$. The number $10^{2021}-1$ is of the form 99...9 and is divisible by 9, while the number 2020 is not. Therefore, their difference is not divisible by 9.