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

Yong Zhang, Arman Shamsi Zargar

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…