  In this article, we are interested in whether a product of three consecutive
integers $a (a+1) (a+2)$ divides another such product $b (b+1) (b+2)$. If this
happens, we prove that there is some gaps between them, namely $b \gg \frac{a
\log a)^{1/6}}{\log \log a)^{1/3}}$. We also consider other polynomial
sequences such as $a^2 (a^2 + l)$ dividing $b^2 (b^2 + l)$ for some fixed
integer $l$. Our method is based on effective Liouville-Baker-Feldman theorem.
