This analysis reveals regular polynomial diophantine triples, suggesting limits on their extension to quadruples.
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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Janaki et al. (2025) studied this question.
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