Survey of divisibility sequences

We call a sequence of rational integers ($a_n$) a divisibility sequence if $a_m$ divides $a_n$ whenever $m$ divides $n$. The divisibility sequence appears in natural way in coordinates of points $nP$ on elliptic curve, where $P$ is a point of infinite order. In general we can define divisibility sequences for arbitrary group scheme over $\mathbb{Z}$. On the lecture we will focus on elliptic case. We will describe main properties and recent results and we will discuss some open problems.