Harristotelian Logic

I fear that mathematicians as a community are capable of lying to the public on a huge scale, and it's hard to show that as they protect each other, so I go to another mathematically sophisticated community to present what looks to me like a way to factor which invalidates the current Internet security system.

You can easily check the math yourself, and then consider the charge that the math community is willfully ignoring this information—leaving you and many others vulnerable—because they are cons finally caught in a dangerous game, where they presented factoring as a hard problem, when the solution is what you can see here.

Let

S = (k_1*sqrt(x) + k_2*sqrt(y))*(k_3*sqrt(x) + k_4*sqrt(y))

and

T = (k_1*sqrt(x) - k_2*sqrt(y))*(k_3*sqrt(x) - k_4*sqrt(y))

now multiply both out, which gives

S = k_1*k_3*x + (k_2*k_3 + k_1*k_4)*sqrt(xy) + k_2*k_4*y

and

T = k_1*k_3*x - (k_2*k_3 + k_1*k_4)*sqrt(xy) + k_2*k_4*y

and now subtract one from the other for one result, and add one to the other for another:

S - T = 2*(k_2*k_3 + k_1*k_4)*sqrt(xy)

and

S+T = 2*k_1*k_3*x + 2*k_2*k_4*y

and if you have an S number and a target composite T to factor, you have two equations with 6 other unknowns with which to determine values that will work.

It seems to me that letting xy be a square of a factor of S-T, might be useful, which can give you x and y as squares, then you have to pick two of the k's, and the final two are determined by the two equations.

AT the end of that bit of work you are mathematically guaranteed—by remarkably basic algebra—to have the factorization

T = (k_1*sqrt(x) - k_2*sqrt(y))*(k_3*sqrt(x) - k_4*sqrt(y))

of your target composite.

And there is nothing in the algebra that says that if T is your public key, this method will not work!

It's basic algebra.

If I am right, then mathematicians will do—nothing.

If they acknowledge my research they are outed as frauds as I am a vocal critic of that community with other major research which they have ignored.

But them doing nothing—if you do nothing as well—is just leaving the door open for someone to do something with the research.

It's your choice.

Do something, or wait, in denial of your own mathematical ability, and see what happens.