On the Diophantine equation $f(x)f(y)=f(z)^n$ involving Laurent   polynomials
  By the theory of elliptic curves, we investigate the nontrivial rational parametric solutions of the Diophantine equation $f(x)f(y)=f(z)^n$, where $n=1,2$ and $f(X)$ are some simple Laurent polynomials. 
Yong Zhang
math.NT