Non-Extendability of Diophantine Triples Comprising Centered Square Numbers

Abstract

In this chapter, three non-extendable Diophantine triples comprises of centered square numbers such that the product of any two members and increased by a non-zero integer or a polynomial with integer co-efficient is a perfect square are exhibited. More precisely, three non-extendable Diophantine triples of the form {a, b, 2(a+b-Square of the difference of the ranks)} involving centered square numbers with property  D(-Square of the difference of the ranks) .