Multiplicative order not

[Joerg Arndt]

* koh <zbi74583 at boat.zero.ad.jp> [Jun 05. 2008 17:43]:
> [...]
> > 
> > The number and length of cycles is also of some relevance
> > when considering the structure of digraphs under quadratic maps in Z/pZ
> > as used in the Lucas-Lehmer tests for primality of Mersenne, Fermat
> > and Wagstaff primes.
> > 
> 
>     I don't understand well.
>     Could you explain more about the relationship between the number and length of cycles and quadratic maps or Lucas-Lehmer test?

See the paper mentioned below, it is this one:

Troy Vasiga, Jeffrey Shallit:
On the iteration of certain quadratic maps over $\GF(p)$
Discrete Math., vol.277, 219-240, 2004
http://www.cs.uwaterloo.ca/~shallit/papers.html

> 
>     
> > There is a paper by Shallit and Vasiga, "...iteration of certain
> > quadratic maps..."
> > with some nice pictures of digraphs.
> > (but there are not only cycles, but also trees and exterior nodes
> > attached to the cycles)

cheers,   jj