Malaysian Journal of Mathematical Sciences, May 2018, Vol. 12, No. 2
On the Some Non Extandable Regular \(P_{-2}\) Sets
Ozen OZER
Corresponding Email: ozenozer39@gmail.com
Received date: 21 November 2017
Accepted date: 29 May 2018
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.
Keywords: \(P_k\)-Sets, Pell Equations, Fundamental Solutions, Residue Classes, Congruences, Legendre/Jacobi Symbol
