Re: Surrogate Factoring Solution
jstevh_at_msn.com
Date: 03/10/05
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Date: 10 Mar 2005 03:50:11 -0800
jstevh@msn.com wrote:
> My apologies up front, as I have the solution now, so it makes sense
to
> start a new thread, though I wonder about the sense of posting an
> actual solution.
>
> It turns out that solving for A and y is key to that solution, as
> remember
>
> yx^2 + Ax - M^2 = 0
>
> and
>
> yz^2 + Az - j^2 = 0,
>
> so
>
> A = (z^2 M^2 - x^2 j^2)/xz(z-x)
>
> and
>
> y = -(zM^2 - xj^2)/zx(z-x)
>
> and focusing again on y/A^2, which I have an algorithm for
calculating,
> I have
>
> y/A^2 = -xz(z-x)(zM^2 - xj^2)/(z^2 M^2 - x^2 j^2)^2
>
> and focusing on the denominator, I wish to know what to multiply
>
> 8j^2 M^2(y/A^2)
>
> times so that it is an integer, so assuming x has a single prime
factor
> of M that I'll call g_1, so x = g_1, and using g_2 = M/g_1, I have
>
> y/A^2 = -g_1^2 z(z - g_1)(zg_2^2 - j^2)/g_1^4(z^2 g_2^2 - j^2)^2
>
> which is
>
> y/A^2 = -z(z - g_1)(zg_2^2 - j^2)/g_1^2(z^2 g_2^2 - j^2)^2
>
> and now focusing on
>
> z^2 g_2^2 - j^2, I can just let
>
> n = z^2 g_2^2 - j^2, and solve for z, so
>
> z = sqrt(n + j^2)/g_2^2
>
Oh yeah that's just ugly wrong. Worse you do it right and n = T fits,
and I've tried that before, as what happens is that if z has g_1 as a
factor, which it does with n = T, then you just end up with y/Az^2
having M in the denominator.
At this point it's not even really brainstorming anymore.
Oh well, that happens in problem solving. After you have the idea
phase you come back and critique, and sometimes no matter how hard you
push, you just can't settle things.
The difference between me and the people who obessively, and notice
quite failingly, reply to my posts, is that I can recognize when a
strategy isn't working.
Well with that said, nothing to do now but consider other things, and
for your amusement you have the replies of some of those posters who
still can't get a clue.
They keep trying, and trying, and trying...
And notice how *happy* they get with my very obvious errors.
These people are entertaining in their own right, so read over their
replies in this thread with a bit more understanding this time.
They can't figure out when an approach doesn't work, so they just keep
trying it.
But I'm giving up on this particular approach, as I'm making arguments
now that have those very stupid errors that tell you you're just
pushing against a wall, and that hope is overpowering reason.
James Harris
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