On the matrix negative Pell equation

Aleksander Grytczuk; Izabela Kurzydło

ArticleOriginal scientific text

Title

On the matrix negative Pell equation

Authors ¹, ¹

Affiliations

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

Abstract

Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn)

\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I

with d ∈ N for nonsingular

X_{i}, Y_{i} \in M ₂ (Z)

, i=1,...,n.

Keywords

ENG

the matrix negative Pell equation, powers matrices

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Title

On the matrix negative Pell equation

Affiliations

Abstract

Keywords

Bibliography