Some Non-Extendable Special Diophantine Triples Involving Nonagonal Pyramidal Numbers
Explorations in Diophantine Equations,
11 November 2023
,
Page 76-85
https://doi.org/10.9734/bpi/mono/978-81-967488-3-8/CH9
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.
- Special Diophantine triples
- pyramidal numbers
- polynomials
- Pell equation
- Special Dio Quadruple