Enticing Sequences of Polynomial Diophantine Triple

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Published: 2025-07-28
Keywords:
polynomial diophantine triples, regular diophantine triple, vieta polynomial, vieta-pell polynomial, vieta-pell lucas polynomial

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G. Janaki
Associate Professor, PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu
R. Sarulatha
Ph.D. Research Scholar, PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu

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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Vol. 9 No. 4 (2025)

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Articles
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