Non-extendable Rational Diophantine 3-tuples Comprising Polynomialsand Special Figurate Numbers

Authors

  • V Sangeetha Department of Mathematics National College (Autonomous) (Affiliated to Bharathidasan University), Trichy - 620 001, Tamil Nadu, India.
  • T Anupreethi * Department of Mathematics National College (Autonomous) (Affiliated to Bharathidasan University), Trichy - 620 001, Tamil Nadu, India.
  • Manju Somanath Department of Electrical Mathematics, National College (Autonomous) (Affiliated to Bharathidasan University), Trichy - 620 001, Tamil Nadu, India.

https://doi.org/10.22105/opt.v2i2.77

Abstract

A rational Diophantine 3-tuple is a family of three non-zero rationals x, y, z with the property D(n) such
that xy + n, yz + n, xz + n are perfect squares. In this paper, a pair of rational polynomials and some
special figurate numbers are scrutinized for their extension as triples and are proved to be non-extendable
as quadruples.

Keywords:

Diophantine triples, Diophantine quadruples, Regular rational Diophantine triples, Irregular rational diophantine quadruples

References

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Published

2025-04-03

Issue

Vol. 2 No. 2 (2025): OPT

Section

Articles

How to Cite

Sangeetha, V., Anupreethi, T., & Somanath, M. (2025). Non-extendable Rational Diophantine 3-tuples Comprising Polynomialsand Special Figurate Numbers. Optimality, 2(2), 78-83. https://doi.org/10.22105/opt.v2i2.77