# Generalized Pell Numbers

1. Mar 27, 2005

### T.Rex

Hi,
In the following document: Generalized Pell Numbers, I've defined what I call "Generalized Pell Numbers".
They provide a way for computing: $$1+\sqrt[m]{m}$$.

I'd like to know if these numbers are already known or not, and if someone knows about other properties they have or if someone is interested to look after new properties.

My main goal is to get more information about the period of Pell Numbers modulo a prime number. So my hope is that these Generalized Pell Numbers will lead to something that could help me.

If you know about properties of Pell numbers modulo a prime number, just let me know !

Tony

2. Mar 28, 2005

### T.Rex

More interesting info: primality test for Fermat numbers ?

Hi,

I've added more information in the paper. A preliminary study seems to show that all these numbers share interesting properties modulo a prime number (including a Fermat prime number) that could lead to a primality test, once proofs are provided ...

Tony