Old and new families of strong Skolem Starters

TL;DR

This paper introduces new families of strong Skolem starters for specific cyclic groups, expanding the known constructions for groups of the form rac{rac{Z}_{p^n}}{rac{rac{Z}_{pq}} with primes p,q rac{1}{8} and n>1.

Contribution

It presents novel constructions of strong Skolem starters for rac{rac{Z}_{p^n}}{rac{rac{Z}_{pq}} groups with infinitely many primes p,q rac{1}{8} and integer n>1.

Findings

New families of strong Skolem starters for rac{rac{Z}_{p^n}}{rac{rac{Z}_{pq}} groups.

Existence of strong Skolem starters for infinitely many primes p,q rac{1}{8} and n>1.

Enhanced understanding of the structure of Skolem starters in cyclic groups.

Abstract

In this paper, we give new families of strong Skolem starters for $\mathbb{Z}_{p^n}$ and $\mathbb{Z}_{pq}$, for infinitely many odd primes $p,q\equiv1$ (mod 8) and $n>1$ be an integer.