BG-MO 1974 Problem 1

Find all natural numbers n with the following property: there exists a permutation $(i_1,i_2,\ldots,i_n)$ of the numbers $1,2,\ldots,n$ such that, if on the circular table there are $n$ people seated and for all $k=1,2,\ldots,n$ the $k$ -th person is moving $i_n$ places in the right, all people will sit on different places.

V. Drenski