7.4. What can be the sum of the digits of a number divisible by 7?
Answer. Any natural number, greater than or equal to 2.

Solution. Note that the numbers 21 and 1001 are divisible by 7, and the sums of their digits are 3 and 2, respectively. Therefore, to get a sum of digits equal to an even number $n$, we need to take a number whose decimal representation consists of $\frac{n}{2}$ groups of digits 1001. Accordingly, to get a sum of digits equal to an odd number $2n+1$, we need to take a number whose decimal representation consists of $\frac{n}{2}-1$ groups of digits 1001 and one group of digits 21. A sum of digits equal to 1 cannot be obtained, because powers of ten are not divisible by 7.