Development of Non-Stretchable Triples with Numerable Features

Abstract

In this paper, some non-extendable triples involving Rook Polynomials, Hermite Polynomials and Laguerre Polynomials with appropriate properties are accomplished. Besides, it is showed that these triples cannot be prolonged into quadruples with the help of property of congruence.

Introduction

Conclusion

In this paper, Diophantine triples comprising Rook polynomials, Hermite Polynomials and Laguerre Polynomials are presented. Also, all these triples cannot be stretched into quadruple is proved by using the basic concepts of congruence. In this manner, one can search triples, quadruples etc with fascinating conditions.

References

[1] Carmichael, R.D. History of Theory of numbers and Diophantine Analysis, Dover Publication, Newyork, 1959. [2] Mordell, L.J. Diophantine equations, Academic press, London, 1969. [3] Dujella, A. \\\"Diophantine quadruples for squares of Fibonacci and Lucas numbers.\\\" Portugaliae Mathematica, vol. 52, issue 3, pp.305-318, 1995. [4] Gopalan, M. A., S. Vidhyalakshmi, and S. Mallika. \\\"Research Article Special family of Diophantine Triples\\\", Scholars Journal of Engineering and Technology (SJET), vol. 2, issue 2A, pp.197-199, 2014. [5] Gopalan, M.A, Vidhyalakshmi, S. and Thiruniraiselvi, N., “Some non-extendable diophantine triples in special number patterns”, International Journal of Innovative research and Review, vol. 2, issue 3, pp. 1-7, 2014. [6] Gopalan, M. A., S. Vidhyalakshmi, and N. Thiruniraiselvi. \\\"A special Diophantine quadruple with property D (17)\\\", IJMTT, vol. 20, issue 2, pp. 110-112, 2015. [7] Saranya, C., and G. Janaki. \\\"Some Non-extendable Diophantine Triples involving Centered square numbers”, International Journal of Scientific Research in Mathematical and Statistical Sciences, vol. 6, pp. 105-107, 2019. [8] P. Sandhya V. Pandichelvi, “Fabrication of Gorgeous Integer Quadruple”, Journal of Engineering, Computing and Architecture, vol. 10, issue 4, pp.115-123, 2020. [9] Saranya, S., and V. Pandichelvi. \\\"Classification of an exquisite Diophantine 4-tuples bestow with an order\\\", Malaya Journal of Matematik (MJM), vol. 9, issue 1, pp. 612-615, 2021. [10] Pandichelvi, V., and B. Umamaheswari. \\\"Appraisal of Integer Quadruples with Graceful Property\\\", Journal of Xi’an Shiyou University, Natural Science Edition, vol. 17, issue 6, pp. 139-149. [11] Sandhya, P., and V. Pandichelvi. \\\"Demonstration of Two Disparate Structures of Integer Triples Concerning Pan-San and Pan-San Comrade Numbers\\\", Advances and Applications in Mathematical Sciences, vol. 21, issue 7, pp. 3921-3930, 2022.

Copyright

Copyright © 2023 V Pandichelvi, R Vanaja. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.