IMO 1983 LL SPA57

Origin: SPA

Problem

In the system of base n2 + 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 n2 + 1, none of them being zero. (iii) If s(C) denotes the number in base n2 + 1 obtained by applying the permutation s to the n digits of the number C, then for each permu- tation s, s(N) = ns(N ′).