Question 99
Call a natural number *twistable* if it does not contain digits $3$, $4$, $7$ and its last digit is not zero. The *twisting* of a twistable number is the number obtained after the following two steps:
* Reverse the order of digits of the given number;
* Twist each digit: $0$, $1$ and $8$ remain unchanged, $2$ and $5$ are turned into each other, $6$ and $9$ are turned into each other.
For instance, the twisting of the number $68012$ is $51089$ and the twisting of the number $69$ is $69$.
Find all integers that can be represented as the ratio of a twistable positive integer $n$ and its twisting $k$.
* Reverse the order of digits of the given number;
* Twist each digit: $0$, $1$ and $8$ remain unchanged, $2$ and $5$ are turned into each other, $6$ and $9$ are turned into each other.
For instance, the twisting of the number $68012$ is $51089$ and the twisting of the number $69$ is $69$.
Find all integers that can be represented as the ratio of a twistable positive integer $n$ and its twisting $k$.