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J. Moussounda Mouanda, On Matrix Solutions in of the Diophantine Equation https://www.researchgate.net/publication, 2022.

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Article

On Beal's Conjecture for Matrix Solutions and Multiplicative Commutative Groups of Rare Matrices

1Blessington Christian University, Mathematics Department Nkayi, Republic of Congo


Turkish Journal of Analysis and Number Theory. 2024, Vol. 12 No. 1, 1-7
DOI: 10.12691/tjant-12-1-1
Copyright © 2024 Science and Education Publishing

Cite this paper:
Joachim Moussounda Mouanda. On Beal's Conjecture for Matrix Solutions and Multiplicative Commutative Groups of Rare Matrices. Turkish Journal of Analysis and Number Theory. 2024; 12(1):1-7. doi: 10.12691/tjant-12-1-1.

Correspondence to: Joachim  Moussounda Mouanda, Blessington Christian University, Mathematics Department Nkayi, Republic of Congo. Email: mmoussounda@yahoo.fr

Abstract

We introduce a new family of Toeplitz matrices called Rare matrices. We construct multiplicative commutative groups of Rare matrices and we establish connections with circulant matrices. We show that, in general, for every positive integer , the equation has an infinite number of matrix triple solutions with the matrices A, B and C do not have a common matrix factor. In other words, Beal's conjecture is not always true for matrix solutions. Mathematics Subject Classification(2010) 15A24, 11D72, 15A16, 11A51.

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