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

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 $g$.

7 pages. Submitted for publication. arXiv admin note: substantial text overlap with arXiv:1608.03810