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Bull. Korean Math. Soc. 2021; 58(3): 609-616

Online first article February 22, 2021      Printed May 31, 2021

https://doi.org/10.4134/BKMS.b200403

Copyright © The Korean Mathematical Society.

Fermat's equation over 2-by-2 matrices

Mao-Ting Chien, Jie Meng

Soochow University; Pusan National University

Abstract

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We study the solvability of the Fermat's matrix equation in some classes of 2-by-2 matrices. We prove the Fermat's matrix equation has infinitely many solutions in a set of 2-by-2 positive semidefinite integral matrices, and has no nontrivial solutions in some classes including 2-by-2 symmetric rational matrices and stochastic quadratic field matrices.

Keywords: Fermat's matrix equation, commuting family of matrices, stochastic matrices

MSC numbers: Primary 15A24, 11D41

Supported by: Jie Meng was partially supported by National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (NRF-2017R1A5A1015722)

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