On the matrix negative Pell equation

Aleksander Grytczuk; Izabela Kurzydło

Discussiones Mathematicae - General Algebra and Applications, Tome 29 (2009), p. 35-45 / Harvested from The Polish Digital Mathematics Library

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Résumé

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.

Publié le : 2009-01-01

Zbl 1196.15013

EUDML-ID : urn:eudml:doc:276938

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Aleksander Grytczuk; Izabela Kurzydło. On the matrix negative Pell equation. Discussiones Mathematicae - General Algebra and Applications, Tome 29 (2009) pp. 35-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1150/

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