What type of study is this?

This is a Quantitative Study study.

October 11, 2025

Enticing Sequences of Polynomial Diophantine Triple

Key Points

The study shows that infinite sequences of polynomial diophantine triples are regular.
Findings include that these triplets cannot be extended to form quadruples.
The analysis utilizes Vieta polynomials, specifically the Vieta-Pell and Vieta-Pell-Lucas forms.
Numerical calculations are performed using MATLAB to derive the findings.

Abstract

This paper examines the establishment of an infinite sequences of polynomial Diophantine triples and substantiates that these sequences comprising of triplets is regular and cannot be extended into a quadruple. The findings are derived from the Diophantine pair formed by Vieta polynomials, specifically the Vieta-Pell and Vieta-Pell-Lucas polynomial. The numerical values are meticulously calculated using MATLAB. 2020 mathematical sciences classification: 11C08

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Cite This Study

Janaki et al. (Mon,) studied this question.

synapsesocial.com/papers/68e9b1c9ba7d64b6fc132626 https://doi.org/https://doi.org/10.64938/bijri.v9n4.25.jl066