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A system of relative Pellian equations and a related family of relative Thue equations

In this paper we consider the family of systems (2c + 1)U^2 - 2cV^2 = μ and (c - 2)U^2 - cZ^2 = -2μ of relative Pellian equations, where the parameter c and the root of unity μ are integers in the same imaginary quadratic number field. We show that for |c| ≥ 3 only certain values of μ yield solutions of this system, and solve the system completely for |c| ≥ 1544686.

Thue equation; quadratic fields

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