A Perusal of Special Polygonal Numbers in Relation to Nasty Numbers of the form \(6A^2\) A \(\in\) Z\(^+\)

N. Thiruniraiselvi; M. A. Gopalan; Sharadha Kumar

doi:10.9734/bpi/mcsru/v5/5578

A Perusal of Special Polygonal Numbers in Relation to Nasty Numbers of the form \(6A^2\) A \(\in\) Z\(^+\)

Authors

N. Thiruniraiselvi Department of Mathematics, Shrimati Indira Gandhi College, Affiliated to Bharathidasan University, Trichy-620 002, Tamil Nadu, India. https://orcid.org/0000-0003-4652-3846
M. A. Gopalan Department of Mathematics, Shrimati Indira Gandhi College, Affiliated to Bharathidasan University, Trichy-620 002, Tamil Nadu, India. https://orcid.org/0000-0003-1307-2348
Sharadha Kumar Department of Mathematics, National College, Affiliated to Bharathidasan University, Trichy- 620 001, Tamil Nadu, India. https://orcid.org/0000-0002-0509-6158

DOI:

https://doi.org/10.9734/bpi/mcsru/v5/5578

Keywords:

Equation, polygonal numbers, integer, nasty numbers

Abstract

This chapter is concerned with different patterns for finding the ranks of special polygonal numbers such that each of these m-gonal numbers, added or subtracted with non-zero integers, represents a square integer multiplied by six. The recurrence relation satisfied by the ranks of respective m-gonal numbers is presented. In addition, the method of determining the unequal ranks of two different polygonal numbers such that their linear combination is a square multiple of six has been exhibited.

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Review History

Published

2025-05-23

How to Cite

N. Thiruniraiselvi, M. A. Gopalan, & Sharadha Kumar. (2025). A Perusal of Special Polygonal Numbers in Relation to Nasty Numbers of the form \(6A^2\) A \(\in\) Z\(^+\). Mathematics and Computer Science: Research Updates Vol. 5, 134–152. https://doi.org/10.9734/bpi/mcsru/v5/5578

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Issue

Mathematics and Computer Science: Research Updates Vol. 5

Section

Chapters