This seemingly simple viral problem is a lot harder than it looks--it is actually a problem from a university level mathematics textbook! In order to solve the problem, we take a journey through symmetry and group theory which leads to a simple formula for solving these kinds of equations.

Thanks to all patrons! Special thanks this month to: Kyle, Michael Anvari, Richard Ohnemus, Shrihari Puranik.

0:00 Problem
1:44 Numerical solution
2:37 Symmetric polynomials
4:15 Power sum polynomials
5:03 Elementary symmetric polynomials
5:46 Deriving Girard-Newton identities
8:14 Girard-Newton identities
9:28 Solution

References/alternate methods listed in my blog post
https://wp.me/p6aMk-8z8/#sources

Multiply by lines and introduction to group theory
https://youtu.be/LmVt_KiyDC4

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