A note on strong Skolem starters

Abstract

In 1991, Shalaby conjectured that any additive group $\mathbb{Z}_n$, where $n\equiv1$ or 3 (mod 8) and $n \geq11$, admits a strong Skolem starter and constructed these starters of all admissible orders $11\leq n\leq57$. Only finitely many strong Skolem starters have been known. Recently, in [O. Ogandzhanyants, M. Kondratieva and N. Shalaby, \emph{Strong Skolem Starters}, J. Combin. Des. {\bf 27} (2018), no. 1, 5--21] was given an infinite families of them. In this note, an infinite family of strong Skolem starters for $\mathbb{Z}_n$, where $n\equiv3$ mod 8 is a prime integer, is presented.