Note on a Problem of Krasikov and Schِnheim for Planar Cyclic Difference Sets

Let D be a planar cyclic difference set with 0 ∈ D. Krasikov and Schönheim proposed in [2] the problem: prove that there are elements di, dj, dk ∈ D − {0} such that di + dj + dk = 0. We prove this and a little more.