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From: JSH on 4 Nov 2009 21:53
You people need to wake up. I'm telling you the underlying math is
EASY. It's a technique to solve quadratic residues modulo N.

If you think it's not possible then use all of your mathematical
training to explain the second example:

So now let's do, k=9. So q = 11 mod 35, and T = 22 mod 35, so I can
try T = 57.

The trivial factorization didn't work here, so I'll just jump to, f_1
= 19, and f_2 = 3, so:

k = 3^{-1}(19 + 3) mod 35 = 12(22) mod 35 = 264 mod 35 = 19 mod 35.

19^2 = 11 mod 35

so it worked! (It's so weird though watching it. Even though I know
the underlying mathematics it seems like magic.)

And that is a factoring example, as I know k=9 is a solution, so I
have

19^2 = 9^2 mod 35

so (19-9)(19+9) = 0 mod 35, so (10)(28) = 0 mod 35, and you pull 5 and
7 as factors with a gcd.

THAT is how you use a method for solving quadratic residues modulo N:
you find one quadratic residue and then go looking for another.

Factoring problem solved.

Happy one year birthday to the solution as it's a year old about now.


James Harris
From: Mark Murray on 5 Nov 2009 03:23
JSH wrote:
> Factoring problem solved.

Where is the complexity analysis?

M
--
Mark Murray
From: amzoti on 5 Nov 2009 14:12
On Nov 4, 6:53 pm, JSH <jst...(a)gmail.com> wrote:
>
> James Harris

I couldn't get passed the title of this thread.

You should stay away from scary things!

It is even scarier to think that you believe you have solved the
factoring problem.

You are still clueless after 15 years and counting.

Delusional narcissist!

From: bert on 5 Nov 2009 16:55
On 5 Nov, 08:23, Mark Murray <w.h.o...(a)example.com> wrote:
> JSH wrote:
> > Factoring problem solved.
>
> Where is the complexity analysis?

James seldom responds to replies which invite
him to do any more work. When he does, it is
usually with some woolly argument as to why
that extra work is unnecessary or inadvisable.
--
From: Mark Murray on 5 Nov 2009 18:51
bert wrote:
> On 5 Nov, 08:23, Mark Murray <w.h.o...(a)example.com> wrote:
>> JSH wrote:
>>> Factoring problem solved.
>> Where is the complexity analysis?
>
> James seldom responds to replies which invite
> him to do any more work. When he does, it is
> usually with some woolly argument as to why
> that extra work is unnecessary or inadvisable.

In a very recent post, he expressed the desire for others to do this extra
work. This was in the context of factoring large numbers.

M
--
Mark Murray
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