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Survey of divisibility sequences

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Krzysztof Gornisiewicz
Adam Mickiewicz U Poznan/MPI
Mit, 15/12/2010 - 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

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.

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