A note on strong Skolem starters

Abstract

In 1991, Shalaby conjectured that any additive group Zn, where n≡1 or 3 (mod 8) and n≥11, admits a strong Skolem starter and constructed these starters of all admissible orders 11≤n≤57. Only finitely many strong Skolem starters have been known. Recently, in Ogandzhanyants et al. (2019) was given infinite families of them. In this note, an infinite family of strong Skolem starters for Zn, where n≡3 (mod 8) is a prime integer, is presented.