----- Original Message -----
From: Wojciech Florek <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, February 01, 2000 12:43 PM
Subject: Mersenne: Re: Is it new? (fwd)
> >Playing with factors of mersennes I've found the following
> >relation:
> >
> >Let p=4q+b, b=1,3, and a=4-b (so a=3,1, respectively) then
> >p divides M(p-3)-aq.
> >E.g.
> >p=41, q=10 b=1 a=3
> >M(38)-3*10=274877906913=6704339193*41
> >
> >p=43, q=10, b=3 a=1
> >M(40)-10=1099511627775=25570037855*43
> >
> >Is it something new or well known?
>
> I don't know. I'm much more a computer programmer than a mathematician.
> You might ask on the Mersenne mailing list. Perhaps someone there can
> answer your question, prove your observation, and tell us if it is of any
> value.
>
> Best regards,
> George
>
If p=1 mod 4 then let x=2^(p-3)-1-3(p-1)/4
so 4x=2^(p-1)-4-3(p-1)=1-4+3=0 mod p.
If p=3 mod 4 then let x=2^(p-3)-1-(p-3)/4
so 4x=2^(p-1)-4-(p-3)=1-4+3=0 mod p.
Yea, it works for any odd prime - you could
prove it more consisely. I cannot see how
this helps to factor Mersennes though.
Rgds,
----------------------------------------------------------
Daniel W. Grace
e-mail: [EMAIL PROTECTED]
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