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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) with d ∈ N
for nonsingular , i=1,...,n.
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