Question 22
Determine all positive integers $n$ such that there exist positive integers $a$ and $b$ which satisfy
$$
S(a) = S(b) = S(a + b) = n.
$$
Here $S(a)$ denotes the sum of digits of $a$. (Romania 1999)
$$
S(a) = S(b) = S(a + b) = n.
$$
Here $S(a)$ denotes the sum of digits of $a$. (Romania 1999)