On strong Skolem starters

Abstract

In this note we present an alternative (simple) construction of cardioidal starters (strong and Skolem) for ${\mathbb{Z}}_{q^n}$, where $q\equiv 3$ (mod 8) is an odd prime number and $n\ge 1$ is an integer number; also for ${\mathbb{Z}}_{pq}$ and ${\mathbb{Z}}_{p^n}$, for infinitely many odd primes $p,q\equiv 1$ (mod 8) and $n\ge 1$ an integer number. This cardioidal starters can be obtained by a more general result given by Ogandzhanyants et al. [O. Ogandzhanyants, M. Kondratieva and N. Shalaby, \emph{Strong Skolem starters}, J. Combin. Des. {\bf 27} (2018), no. 1, 5--21].