  For a binary quartic form $\phi$ without multiple factors, we classify the
quartic K3 surfaces $\phi(x,y)=\phi(z,t)$ whose Neron-Severi group is
(rationally) generated by lines. For generic binary forms $\phi$, $\psi$ of
prime degree without multiple factors, we prove that the Neron-Severi group of
the surface $\phi(x,y)=\psi(z,t)$ is rationally generated by lines.
