Re: Factoring problem, my assertion revisited
rupertmccallum_at_yahoo.com
Date: 02/08/05
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Date: 7 Feb 2005 18:07:43 -0800
jstevh@msn.com wrote:
> Well I can at least give some idea why I figured I'd solved the
> factoring problem, and kept talking about theoretically, while my
> attempts at implementing the theory have so far failed to live up to
> even my expectations:
>
> There are the two quadratics:
>
> yx^2 + Ax - M^2 = 0
>
> and
>
> yz^2 + Az - j^2 = 0
>
> where A, j, and M are integers greater than 0 chosen, where M is the
> target to be factored, and that is done through factoring the
surrogate
> T, which is
>
> T = M^2 - j^2
>
> and substituting out y to solve for x and z gives
>
> x = z(-Az +/- sqrt((Az - 2M^2)^2 - 4TM^2))/(2j^2 - 2Az)
>
> and
>
> z = x(-Ax +/- sqrt((Ax - 2j^2)^2 - 4Tj^2))/(2M^2 - 2Ax)
>
I'm sorry, I don't follow this step. Could you explain it in a bit more
detail?
Also, could you tell me: when you say you think you've solved the
factoring problem, do you mean you think you've found an algorithm
which you can prove will factor an arbitrary positive integer in
polynomial time?
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