GENERALIZED PELL EQUATIONS FOR 2 × 2 MATRICES
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2017, Vol 37, Issue 1
Abstract
In this paper we consider the solutions of the generalized matrix Pell equations X^2 − dY^2 = cI, where X and Y are 2 × 2 matrices over Z, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity matrix. We determine all solutions of such equations for c = ±1, as well as all non-commutative solutions for an arbitrary c.
Authors and Affiliations
Boaz Cohen
Keywords
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