摘要 :
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 ...
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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 K = Q((-d)~(1/2)). We show that for |c| ≥ 3 only certain values of μ yield solutions of this system, and solve the system completely for |c| ≥ 1544686. Furthermore we will consider the related relative Thue equation X~4 - 4cX~3Y + (6c + 2)X~2Y~2 + 4cXY~3 + Y~4 = μ and solve it by the method of Tzanakis under the same assumptions.
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摘要 :
Let c be a positive integer. In this paper, we use themethod of Tzanakis to transform the quartic Thue inequality-4x~3y-(2c-2)x~2y~2+(4c + 4)xy~3-(2c1)y~4|max {c/4 , 4}into systems of Pellian equations. Then we find all primitive ...
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Let c be a positive integer. In this paper, we use themethod of Tzanakis to transform the quartic Thue inequality-4x~3y-(2c-2)x~2y~2+(4c + 4)xy~3-(2c1)y~4|max {c/4 , 4}into systems of Pellian equations. Then we find all primitive solutions ofthis inequality using continued fractions.
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