2. A 200-digit natural number had one of its digits erased. As a result, the number decreased by 5 times. Find all numbers for which this is possible.
Answer: $125 a \cdot 10^{197}$ for $a=1,2,3$.

Solution. Represent the original number in the form $m+10^{k} a+10^{k+1} n$, where $a$ is a decimal digit, $k, m$, $n$ are non-negative integers, and $m<10^{k}$. Therefore, $a$ will be the leading digit of the original number, from which $k=199$. Then

$$
4 m=10^{k} a=10^{199} a \Longleftrightarrow m=25 a \cdot 10^{197}
$$

and the original number is $125 a \cdot 10^{197}$. Since $m<10^{199}$, the digit $a$ takes the values $1,2,3$.