The problem is indeed misquoted. Here is the correct statement:

>If a polynomial $P(x)$ with rational coefficients has at least three simple zeros then the equation $y^2z^3=P(x)$ has only finitely many solutions in integers $x,y,z$ with $yz\neq 0$.

The paper can be found [here][1].


  [1]: http://matwbn.icm.edu.pl/ksiazki/aa/aa31/aa3129.pdf