  In a recent paper we proved that if (*)=\inf_{|z_k|=1}\max_{v=1,...,n^2-n}
|\sum_{k=1}^n z_k^v|, then (*)=\sqrt{n-1} if n-1 is a prime power. We proved
that a construction of Fabrykowski gives minimal systems (z_1,...,z_n) to this
problem. The construction depends on the existence of perfect difference sets
of order n-1. As an open problem we asked whether all solutions would arise
from this construction. In this paper we show that this is true and in fact if
there exist no perfect difference set of order n-1 (which by the prime power
conjecture is true if n-1 is not a prime power), then we have the strict
inequality (*)>\sqrt{n-1}.
