3 equations that should have some relationships; 3 equations of this thread so far.

In[14]:= soln = Solve[y == Sqrt[(n*y - x^2)/x], x]

soln //. {n -> 85, y -> 16.85229955} // N

Out[14]= {{x -> 1/2 (-y^2 - Sqrt[4 n y + y^4])}, {x ->

1/2 (-y^2 + Sqrt[4 n y + y^4])}}

Out[15]= {{x -> -288.957}, {x -> 4.95729}}

Sqrt[(85*(85/x) – x^2)/ x] = x

Abs(tan(85 / (2*Pi))) * x + x = 85/(2*Pi) tan in radians of course.

((85^4/x + 2*(85^2 * x^2) + x^5) / 85^3 ) * x – 85 = 0

These 3 equations each approximate x and y when 85 = x * y.

In my program I tested each value from 1 to 85 to see which numbers worked for x.

There is some error, but it x should approximately equal 5.

N = p *q or N = x * y.

I cannot solve the polynomial to find x from only knowing N. But when you test y proves the equation works.

The trouble is it is not so much different from factoring. No speed increase. But it is a legitimate equation. I am researching new ways to solve polynomials.

Any more questions just ask or see my site: www.constructorscorner.net

There is a link on the Homepage ?

A more descriptive picture.

Sqrt[(85*(85/x) – x^2)/ x] = y

Abs(tan(85 / (2*Pi))) * x + x = 85/(2*Pi) tan in radians of course.

((85^4/x + 2*(85^2 * x^2) + x^5) / 85^3 ) * x – 85 = 0

________ These three equations solve show how two Prime numbers x and y equal 85.

This is important because in asymmetric cryptography such as RSA, the public key is the product of 2 unknown Prime numbers. If we can set a relationship to find x or y when given N, which in this case is 85, the one way function that RSA is based on is mathematically defeated!!!

_______ So if we set equation 1 equal to equation 3 the polynomial produced, if solvable, will solve for x.

Equation used to find 5 knowing 85:

((85^4/x + 2*(85^2 * x^2) + x^5) / 85^3 ) – 0.6 = Sqrt[(85*(85/x) – x^2)/ x] + 0.15

= approximately 5.02 when solved by Wolfram Alpha!

I believe this will defeat RSA. However no one believes me or just doesn’t care. To me it is interesting, but when I ask people about it no response. If it worked I think it would go viral. What do you think?

This is the same post to another community. Either people don’t believe me and my math or they just don’t care about math. I thought that knowing N and solving to find one of its products x could be found knowing only N. (There is no reason that the equations cannot be manipulated to solve for y.)

I’m posting this problem everywhere I can. I believe it has merit. On another message board a math guru showed that x and y (knowing them both) complete the equation. However for every value I have tested, within error, I have found the answer to be in acceptable range of the Prime number we are solving for knowing only 85 (N).

This is as simple as I can make the equations in a page format. I used Wolfram Alpha to solve the polynomial. I have had good results.

There is an error in the approximation within a certain range.

You may not believe me but there is merit to this math write-up.