Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 1, pp. 1-10 (2004)

The diophantine equation $x^4-y^4=z^2$ in three quadratic fields

Sándor Szabó

University of Bahrain

Abstract: Each solution of the equation $x^4-y^4=z^2$ in the integers of the quadratic field $Q(\sqrt{d})$ is also a solution of the equation $xyz=0$, where $d=-2,-1,2$.

Keywords: Diophantine equations, Quadratic fields

Classification (MSC2000): 11F06; 11E08

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