  Let $P(m)$ denote the greatest prime factor of $m$. For integer $a>1$, M. Ram
Murty and S. Wong proved that, under the assumption of the ABC conjecture,
$$P(a^n-1)\gg_{\epsilon, a} n^{2-\epsilon}$$ for any $\epsilon>0$. We study
analogues results for the corresponding divisibility sequence over the function
field $\mathbb{F}_q(t)$ and for some divisibility sequences associated to
elliptic curves over the rational field $\mathbb{Q}$.
