/sci/ - Science & Math

>>10543223
I was getting somewhere, but can't quite connect all the dots. It's part of Hilbert's 17th problem here https://en.wikipedia.org/wiki/Hilbert%27s_seventeenth_problem and here https://en.wikipedia.org/wiki/Positive_polynomial

P(x) must be a sum of two squares of real polynomials in one variable. So it takes the form [math](x+a)^{2}+(x+b)^{2}=2x^{2}+2ax+2bx+a^{2}+b^{2}[/math]

Then find a family of polynomials f sub such that [math]\sum_{j=1}^{k}(f_{j}(x))^{2}=[/math] shares the form for P(x).

Trying f sub j of x equals (j+x) for example gives https://www.wolframalpha.com/input/?i=sum((j%2Bx)%5E2,j,1,k) which is the correct degree, but I didn't check if coefficients jived.

>>10537473
Cancer exists on the physical layer, therefore it can be cured. It's simply an arrangement of molecules. The greater the mastery of nanotechnology, and then the ability to apply it to a body, the closer the cure. Of course at some level you'll just be 3-d printing humans 5th element style, but hey, no more cancer.