Spike Jones wrote:
> A few weeks ago, I thought someone posted something like:
>
> 2^n-1 where n is prime cannot have any factor smaller than n.
>
> Did I get that right? Is there a simple proof? spike
Factors of a mersenne number Mp are always of the form f=2*p*k+1, k may be
as small as 1.
The proof that factors are 2kp+1 is not simple as far as I remember and uses
the theory of quadratic residues (and thus I didn't understand it). See it
on Chris Caldwells (superb) page on Prime numbers,
http://www.utm.edu/research/primes/ .
The proof is at http://www.utm.edu/research/primes/notes/proofs/MerDiv.html
Ciao,
Alex.
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