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.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/246