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

Joachim Moussounda Mouanda^1,

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

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

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.

Keywords:
Matrix equations Diophantine Equations Matrix inversion Factorization

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