Re: Critiquing surrogate factoring

From: C. Bond (cbond_at_ix.netcom.com)
Date: 03/30/05 

Date: Wed, 30 Mar 2005 17:52:55 GMT

jstevh@msn.com wrote:

> The idea is simple enough, factor one number and use its factorization
> to get the factorization of another. The point being taking a number
> that is hard to factor, and yet, factoring it, by factoring an easier
> number.
>
> I thought it might help to try and write the the gist of it in a
> theorem.
>
> Surrogate Factoring Theorem:
>
> Given M, a target natural number to be factored, and j, an integer
> chosen such that j^2>M^2, a rational factor b_2 of M is given by
>
> b_2 f_1 = (-(Az - 2M^2)+/- sqrt((Az - 2M^2)^2 - 4TM^2))/2
>
> where T = M^2 - j^2, and f_1 is a rational factor of T, and where Az is
> given by

If j^2>M^2, as required above, then T is negative. Is that what you want? 

--
There are two things you must never attempt to prove: the unprovable -- and
the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com

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