On the Some Non Extandable Regular P-2 Sets

Abstract

Diophantine 3-tuples with property P-k, for k an integer, are sets of n positive integers such that product of any two of them by adding k is a square. In the present paper, we consider some regular P-k- triples and prove that they can not be extendible to Diophantine quadruple when k = -2 by using fundamental solution of Pell equations. Also, we determine several significant properties about such sets.