OMM 2021 Problem 5

If $n=\overline{a_1a_2\cdots a_{k-1}a_k}$ , be $s(n)$ such that . If $k$ is even, $s(n)=\overline{a_1a_2}+\overline{a_3a_4}\cdots+\overline{a_{k-1}a_k}$ . If $k$ is odd, $s(n)=a_1+\overline{a_2a_3}\cdots+\overline{a_{k-1}a_k}$ For example $s(123)=1+23=24$ and $s(2021)=20+21=41$ Be $n$ is $digital$ if $s(n)$ is a divisor of $n$ . Prove that among any 198 consecutive positive integers, all of them less than 2000021 there is one of them that is $digital$ .