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

Yong Zhang; Arman Shamsi Zargar

paper

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

arXiv:1608.03810

Abstract

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

arXiv comment8 pages. Submitted for publication. Any comments are welcome. arXiv admin note: text overlap with arXiv:1608.03809

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

Abstract

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