Some Non-Extendable Special Diophantine Triples Involving Nonagonal Pyramidal Numbers

Authors

  • S. Vidhya PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.
  • G. Janaki PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.
  • T. Gokila PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

DOI:

https://doi.org/10.9734/bpi/mono/978-81-967488-3-8/CH9

Keywords:

Special Diophantine triples, pyramidal numbers, polynomials, Pell equation, Special Dio Quadruple

Abstract

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 (\(\mathit{p}\), \(\mathit{q}\), \(\mathit{r}\) ) 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.

Published

2023-11-11

How to Cite

S. Vidhya, G. Janaki, & T. Gokila. (2023). Some Non-Extendable Special Diophantine Triples Involving Nonagonal Pyramidal Numbers. Explorations in Diophantine Equations, 76–85. https://doi.org/10.9734/bpi/mono/978-81-967488-3-8/CH9

Issue

Explorations in Diophantine Equations

Section

Contents