Question 24
a. Show that the sum of the digits of the number $10^{n} + 9 n$ is not divisible by 2007 for any natural number $n$.
b. Find at least one natural number $n$ for which the sum of the digits of the number $10^{n} + 9 n$ equals 2008.
b. Find at least one natural number $n$ for which the sum of the digits of the number $10^{n} + 9 n$ equals 2008.