Re: Simple answer, surrogate factoring

jstevh_at_msn.com
Date: 03/05/05 

Date: 4 Mar 2005 17:55:54 -0800

Tim Peters wrote:
> [JSH]
> [...]
> > Check for 169(6972) as a solution to Ax and get back to the group.
>
> No such solution is found. This is what you originally wrote:
>
> # you solve for Ax using
> #
> # Ax = +/-(f_1 - f_2) + 2j^2
> #
> # where f_1 f_2 = Tj^2,
>
> Right or wrong? Ax = 169(6972) can't be obtained from that, so one
or the
> other is wrong:
>

Your reply is not what I expected. It is possible that I made an error
in my calculations, if so, you should have noted it.

If not then you are running up against mathematical absolutes.

Given

z = x(-Ax +/- sqrt((Ax - 2j^2)^2 + 4Tj^2))/(2M^2 - 2Ax)

which follows from

yx^2 + Ax - M^2 = 0

and

yz^2 + Az - j^2 = 0

it MUST be true that every integer solution for Ax is given by
considering factors f_1 and f_2 such that

f_1 f_2 = Tj^2

so the answer has to be there.

It's a mathematical absolute.

So, either I screwed up in caculating Ax with x = 169, or you're doing
something wrong.

I screw up all the time. Check my math. If it's wrong, then that's an
explanation.

If it's not, then despite anything else you might believe, you have to
be doing something wrong.

z = x(-Ax +/- sqrt((Ax - 2j^2)^2 + 4Tj^2))/(2M^2 - 2Ax)

MUST give all the integer solutions for Ax if you iterate properly
through all the factors of Tj^2.

If you are doing something wrong, then everything you have posted up to
this time on this subject is suspect.

The algorithm I have given at this time is perfect.

So you must have at least one mistake.

James Harris

Relevant Pages

  • Re: Simple answer, surrogate factoring
    ... Tim Peters wrote: ... If not then you are running up against mathematical absolutes. ... it MUST be true that every integer solution for Ax is given by ... explanation. ...
    (sci.math)
  • Re: Simple answer, surrogate factoring
    ... Tim Peters wrote: ... and I need 169A to be an integer, so I need the factorization of ... Plugging in 6972, gives ... so you screwed up somewhere as 169is an integer solution for Ax. ...
    (sci.math)
  • Re: Simple answer, surrogate factoring
    ... Tim Peters wrote: ... and I need 169A to be an integer, so I need the factorization of ... Plugging in 6972, gives ... so you screwed up somewhere as 169is an integer solution for Ax. ...
    (sci.crypt)