Some Non-Extendable Special Diophantine Triples Involving Nonagonal Pyramidal Numbers

In this chapter, we discover the special Diophantine triples for the nonagonal pyramidal number with distinct ranks. The chapter mainly focuses on building three separate polynomials with integer coefficients such as the multiple of any two components of the ensemble increased to their total and prolonged by a non-null integer (or a polynomial with integral coefficients) is a perfect square. In addition, the triple is not extended to a quadruple is analyzed. It is concluded that, we can explore for some other Special Diophantine triples for higher order Pyramidal numbers with equivalent fitting properties.