Question 52
Let $n$ be a positive integer with $b$ digits and $l, r$ be non-negative integers satisfying $l + r \lt b$. We say that a positive integer number is a sub-divisor of $n$, if it divides the number obtained by erasing the first $l$ and last $r$ digits of $n$. (For example, sub-divisors of $143$ are $1$, $2$, $3$, $4$, $7$, $11$, $13$, $14$, $43$ and $143$.) For any positive integer $d$, let $A_d$ be the set of positive integers for which $d$ is not a sub-divisor. Find all positive integers $d$ for which the set $A_d$ is finite.