Johan Winge wrote:
> Hello!
> A fairly simple question maybe, but bear with me please...
>
> Am I correct in my assumption that if e.g. p=2*k*p(1)*p(2) divides M(p(1)),
> then p only divides other mersenne numbers with an exponent which is a
> multiple of p(1), (and thus cannot divide M(p(2)) )? Is there a proof for
> this or am I wrong?
You are correct.
This question has come up several times in the past.
Its implied by the fact that GCD(a^m-1,a^n-1) = a^GCD(m,n)-1. This is
proven in an exercise in Knuth in the section on GCD's.
Regards,
Herb Savage
> Regards,
> Johan Winge
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