On Sequences of Geophine Triples Involving Padovan and Bernstein Polynomial with Propitious Property

G Janaki; R Sarulatha

doi:10.17485/IJST/v17i16.160

Article

On Sequences of Geophine Triples Involving Padovan and Bernstein Polynomial with Propitious Property

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i16.160

Year: 2024, Volume: 17, Issue: 16, Pages: 1690-1694

Original Article

On Sequences of Geophine Triples Involving Padovan and Bernstein Polynomial with Propitious Property

G Janaki¹, R Sarulatha^2,3*

¹Associate Professor, PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India
²PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli
³Research Scholar, PG and Research Department of Mathematics, Cauvery College for Women (Autonomous), Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:23 January 2024, Accepted Date:23 March 2024, Published Date:16 April 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: To bring forth a new conception in the time-honoured field of Diophantine triples, namely “Geophine triple”. To examine the feasibility of proliferating an unending sequence of Geophine triples from Geophine pairs with the property comprising Padovan and Bernstein polynomial. Method: Established Geophine triples employing Padovan and Bernstein polynomial by the method of polynomial manipulations. Findings: An unending sequences of Geophine triples and with the property and are promulgated from Geophine pairs, precisely involving Padovan and Bernstein polynomials and few numerical representation of the sequences are computed using MATLAB. Novelty: This article carries an innovative approach of determining this definite type of triples using Geometric mean and thereby, two infinite sequences of Geophine triples with the property are ascertained. Also, few numerical representations of the sequences utilizing MATLAB program are figured out, thus broadening the scope of computational Number Theory.

Keywords: Polynomial Diophantine triple, Geophine triple, Bernstein polynomial, Padovan polynomials, Pell’s equation, Special Polynomials

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Copyright

© 2024 Janaki & Sarulatha. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)