Re: JSH: Key in the lock, factoring technique

On Feb 9, 1:31 pm, JSH <jst...@xxxxxxxxx> wrote:
So guess what? Big new thing is that I came up with this guessing
technique to factor, which is a key in the lock technique, where the
guesses have to be correct or you don't get all integers.

Trouble is, and why I'm still putting out the posts, the math people
are either quiet or still arguing with me, which in this case means
showing complete contempt for your knowledge of basic algebra:

The four equations are:

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = r_1 + k_1*p_1

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = r_2 + k_2*p_2

and

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)


Note however that if you substitute the right
sides of equations 3 and 4 into equation 1, you
get exactly equation 2. The 4 equations are
not independent. You really have only 3 equations
in 4 unknowns.

Which means in general there are infinitely
many solutions. Of course you are only interested
in solutions which are all-integers. So how do you
find those solutions?

The four unknowns are c_1, c_2, d_1, and d_2.
You can set one of them equal to an arbitrary
integer - say, c_1 = 48 - and solve for the others.
In general the solutions are not integers. You could
therefore try another value for c_1, solve again, see
if the solutions are integers.

But in general they are not. How many c_1's must
you try before you find all-integer solutions for the
other unknowns?

Maybe a lot. There is no reason to think the number
is small. And it may that, for a given choice of p_1
and p_2, there is NO integer choice for c_1 which gives
integer solutions for c_2, d_1, and d_2. Which means you
may have to search over various values of p_1 and p_2
also.

Maybe you should try to figure this out before continuing
to claim an efficient solution to the factoring problem.

and that may seem like a LOT of variables (ok, it is) but most of
them
are known as p_1 and p_2 are prime numbers. T is the target composite
to factor, r_1 = T mod p_1, and r_2 = T mod p_2, so k_1 and k_2 are
easily calculated.

And f_1, f_2, g_1, and g_2 are residues where

f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2

so those are you keys to the lock. If you guess right then the last
two equations are true. If you guess wrong, then they are not true
for integers.

That's why this technique is about a key in the lock.

Note, guessing wrong will still give you an answer for the c's and
d's, but not all integers.

You have four equations and four unknowns as if you counted along,
only c_1, c_2, d_1, and d_2 are left as unknowns, and you can see the
four equations.


It's really only 3 equations in 4 unknowns. The solution-space
is infinite in the rationals. You need only the integer solutions.
But how do you find them without checking a huge set of rational
solutions?

Math people have a reason to fight my research, and the point here
is
there are NO LIMITS in their fight so they cannot be the ones who are
telling the truth.

Otherwise, they'd celebrate a great advance.

But I suggest to you they feel fear and are just looking to see if
they can hide the result or if I'll just be ignored.

It's like, if quantum theory and relativity had been blocked by the
physics community because most physicists were fakes so that Einstein,
Schroedinger and Heisenberg had to get creative to get the truth out.

I am being creative but I realize the future still is in doubt.

They will hide the truth because they see truth in mathematics as
their enemy.

The mathematical field was corrupted. And the future of the human
species is in danger as a result.


This is delusional talk. You keep rushing out with one bogus
solution after another, and before you have validated a solution
you start predicting apocalypse. And every time you have done
that you have been wrong. This time is no different. You keep
proving over and over again that you are utterly negligible.

Marcus.


Continued scientific progress is in doubt if the problem is not
addressed as correct mathematics is crucial to it.

James Harris

.

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