Abstract
All Diophantine equations ax 2 + by 2 + cz 2 = 1 + dxyz, with a, b, c, d ∈ N and a| d, b| d, c| d, having solutions ( x, y, z) ∈ N 3 are determined. One particular equation of this type 2 x 2 + 2 y 2 + 3 z 2 = 1 + 6 xyz appeared recently in connection with the description of the lower part of the approximation spectrum for quaternions.
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