On the Diophantine equations $z^2=f(x)^2 \pm g(y)^2$ concerning Laurent polynomials

Yong Zhang; Arman Shamsi Zargar

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arXiv · 1706.02925

On the Diophantine equations $z^2=f(x)^2 \pm g(y)^2$ concerning Laurent polynomials

Yong Zhang·Arman Shamsi Zargar

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Abstract

By the theory of elliptic curves, we study the nontrivial rational parametric solutions and rational solutions of the Diophantine equations $z^2=f(x)^2 \pm g(y)^2$ for some simple Laurent polynomials $f$ and $g$.

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Yong Zhang, Arman Shamsi Zargar. 2017-06-08. On the Diophantine equations $z^2=f(x)^2 \pm g(y)^2$ concerning Laurent polynomials. https://arxiv.org/abs/1706.02925

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