Note on the matrix Fermat’s equation

Aleksander Grytczuk and Izabela Kurzydło
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 17, 2011, Number 2, Page 4—11
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Authors and affiliations

Aleksander Grytczuk
Faculty of Mathematics, Computer Science and Econometrics,
University of Zielona Gora,
65-516 Zielona Gora, Poland

Izabela Kurzydło
Faculty of Mathematics, Computer Science and Econometrics,
University of Zielona Gora,
65-516 Zielona Gora, Poland

Abstract

We consider the Fermat’s equation Xⁿ + Yⁿ = Zⁿ in the set of 2 × 2 rational matrices. We give some necessary condition of solvabillity of this equation.

Keywords

• The matrix equation
• The matrix Fermat’s equation
• Powers of matrices

AMS Classification

• 15A24
• 15A42

References

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