  Erd\"os and Obl\'ath proved that the equation $n!\pm m!=x^p$ has only
finitely many integer solutions. More general, under the ABC-conjecture, Luca
showed that $P(x)=An!+Bm!$ has finitely many integer solutions for polynomials
of degree $\geq 3$. For certain polynomials of degree $\geq 2$, this result
holds unconditionally. We consider irreducible homogeneous $f(x,y)\in
\mathbb{Q}[x,y]$ of degree $\geq 2$ and show that there are only finitely many
$n,m$ such that $An!+Bm!$ is represented by $f(x,y)$. As corollaries we get
alternative proofs for the unconditional results of Luca. We also discuss the
case of certain reducible $f(x,y)$. Furthermore, we study equations of the form
$n!!m!!=f(x,y)$ and $n!!m!!=f(x)$.
