IT-CESENATICO 2023 Problem 3

Let $s(n)$ denote the sum of the digits of $n$ . a) Do there exist distinct positive integers $a, b$ , such that $2023a+s(a)=2023b+s(b)$ ? b) Do there exist distinct positive integers $a, b$ , such that $a+2023s(a)=b+2023s(b)$ ?