ILL 1983 Problem 57

In the system of base $n^2 + 1$ find a number $N$ with $n$ different digits such that:(i) $N$ is a multiple of $n$ . Let $N = nN'.$ (ii) The number $N$ and $N'$ have the same number $n$ of different digits in base $n^2 + 1$ , none of them being zero.(iii) If $s(C)$ denotes the number in base $n^2 + 1$ obtained by applying the permutation $s$ to the $n$ digits of the number $C$ , then for each permutation $s, s(N) = ns(N').$