ON THE SOME PARTICULAR SETS

Abstract

For ?? an integer, a ???? set is defined as a set of ?? positive integers with the property that the product of its any two distinct element increased by ?? is a perfect square integer.In this study, the certain special ???5, ??+5, ???7 and ??+7 sets with size three are considered. It is demonstrated that they cannot be extended to ???5, ??+5, ???7 and ??+7 with size four. Also, some properties of them are proved.