On the Diophantine equations $z^2=f(x)^2 \pm f(y)^2$ involving Laurent   polynomials
  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 $f$. 
Yong Zhang and Arman Shamsi Zargar
math.NT