MathDB

57

Part of 1983 IMO Longlists

Problems(1)

Find a number n in the system of base n^2 + 1

Source:

10/7/2010
In the system of base n2+1n^2 + 1 find a number NN with nn different digits such that:
(i) NN is a multiple of nn. Let N=nN′.N = nN'.
(ii) The number NN and N′N' have the same number nn of different digits in base n2+1n^2 + 1, none of them being zero.
(iii) If s(C)s(C) denotes the number in base n2+1n^2 + 1 obtained by applying the permutation ss to the nn digits of the number CC, then for each permutation s,s(N)=ns(N′).s, s(N) = ns(N').
number theory unsolvednumber theory