Problem

Source: 2020 China North Mathematical Olympiad Advanced Level P5

Tags: number theory, Digits, multiple



Find all positive integers $a$ so that for any $\left \lfloor \frac{a+1}{2} \right \rfloor$-digit number that is composed of only digits $0$ and $2$ (where $0$ cannot be the first digit) is not a multiple of $a$.