Question 28
Prove that for any positive integer $d$ it is possible to find two distinct positive integers $n_1$ and $n_2$ such that
* $n_2$ can be obtained from $n_1$ by permuting its digits,
* both $n_1$ and $n_2$ are divisible by $d$,
* none of them starts with "0".
Denote by $|x|$ the number of digits in $x$. Prove that there exists $d$ such that $|n_1| \gt 2|d|$ for any pair $(n_1, n_2)$ satisfying above properties.
* $n_2$ can be obtained from $n_1$ by permuting its digits,
* both $n_1$ and $n_2$ are divisible by $d$,
* none of them starts with "0".
Denote by $|x|$ the number of digits in $x$. Prove that there exists $d$ such that $|n_1| \gt 2|d|$ for any pair $(n_1, n_2)$ satisfying above properties.