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

Arman Shamsi Zargar; Yong Zhang

arxiv: 1608.03810 · v4 · pith:A4RDGPOXnew · submitted 2016-08-11 · 🧮 math.NT

On the Diophantine equations z²=f(x)² pm f(y)² involving Laurent polynomials

Yong Zhang , Arman Shamsi Zargar This is my paper

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keywords diophantineequationslaurentpolynomialsrationalsolutionscurveselliptic

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

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On the Diophantine equations z²=f(x)² pm f(y)² involving Laurent polynomials

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