On two-quotient strong starters for aq

Abstract

Let G be a finite additive Abelian group of odd order n, and let G^∗= G \ {0} be the set of non-zero elements. A starter for G is a set S = {{xi,yi}: i = 1,..., n-1/2} such that "equ"Moreover, if |{xi+yi: i = 1,...,n-1/2} = n-1/2, then S is called a strong starter for G. A starter 5 for G is a k quotient starter if there is Q G^∗of cardinality k such that yi/xi ∈ Q or xi/yi ∈ Q, for i = 1,..., n-1/2. In this paper, examples of two-quotient strong starters for F, will be given, where q = 2^kt +1 is a prime power with k> 1 a. positive integer and t an odd integer greater than 1. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.