Note on a problem of Krasikov and Schönheim for planar cyclic difference sets (Q1348776)

Let \(D\) be a subset of size \(n+1\) of the cyclic group \(G=C_{n^2+n+1}\) such that every nonidentity \(g\in G\) has precisely one representation \(g=ab^{-1}\) with \(a,b\in D\). For \(d\in D\) there are \(d_1,d_2,d_3\in D\setminus\{d\}\), not all three equal, such that \(d_1d_2d_3=d^3\).