CREATION OF SEQUENCES OF SINGULAR 3-TUPLES THROUGH ABEL AND CYCLOTOMIC POLYNOMIAL WITH COMMENSURABLE PROPERTY


By

R. Vanaja1 and V. Pandichelvi2

1Department of Mathematics, AIMAN College of Arts & Science for Women, Tiruchirappalli, Tamil Nadu,

India-620021

(Aliated to Bharathidasan University)

2Post Graduate & Research Department of Mathematics, Urumu Dhanalakshmi College, Tiruchirappalli,

Tamil Nadu, India-620019

(Aliated to Bharathidasan University)

Email: vanajvicky09@gmail.com, mvpmahesh2017@gmail.com

(Received: June 06, 2022, In format: July 28, 2022; Revised: August 24, 2022; Accepted: April 08, 2023)


DOI: https://doi.org/10.58250/jnanabha.2023.53112


 

Abstract

In this paper, the sequence of 3-tuples named as singular 3-tuples {f (x), g(x), h(x)}, {g(x),  h(x), i(x)} etc. concerning Abel’s polynomial and Cyclotomic polynomial such that the arithmetic mean of any two  polynomials increased by a monomial with integer coefficients provides square of a particular  polynomial is enumerated. Furthermore, Python program for conformation of each of an evaluated  singular 3-tuples is also exemplified.


2020 Mathematical Sciences Classification: 11B83

Keywords and Phrases: Singular 3-tuples, Abel’s polynomial, Cyclotomic polynomial.


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