##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Peter Stevenhagen

#### Universiteit Leiden

## Prime divisors of linear recurrent sequences

##### Abstract:

For many integer sequences $X=(x_n)_n$, it is a natural question to describe the set $P_X$ of all prime numbers $p$ that divide some non-zero term of the sequence, and to quantify the `size' of $P_X$. \\ \noindent We focus on the case of linear recurrent sequences, where we have fairly complete results for recurrences of order 2 based on the Chebotarev density theorem, and mostly open questions for higher order recurrences.

Host: Cristian Popescu

### January 22, 2009

### 1:00 PM

### AP&M 7321

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