Question 16
We say that an integer $m$ covers the number 1998 if $1,9,9,8$ appear in this order as digits of $m$. (For instance, 1998 is covered by 215993698 but not by 213326798.) Let $k(n)$ be the number of positive integers that cover 1998 and have exactly $n$ digits ($n \geqslant 5$), all different from 0. What is the remainder of $k(n)$ in division by 8?