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

Source:

October 7, 2010

number theory unsolvednumber theory

Problem Statement

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').

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