Welcome to the first ever Brilliant Polynomial Roots Contest. This is inspired by many other contests in Brilliant. The aim is to improve the skills of Brilliant users in olympiad problems that ask you to find some functions involving the roots of a polynomial by vieta's, newton sums or other methods. The rules are:
I will post the first problem. If someone solves it, he or she can post a solution and then must post a new problem.
A solution must be posted below the thread of the problem. Then, the solver must post a new problem as a separate thread.
Please make a substantial comment.
Make sure you know how to solve your own problem before posting it, in case no one else is able to solve it within 36 hours. Then, you must post the solution and you have the right to post a new problem.
If the one who solves the last problem does not post a new problem in 24 hours, the creator of the previous problem has the right to post another problem.
No restriction in techniques you can use! use of calculus and roots of unity is allowed. use of cyclotomic polynomials and möbius inversion is also allowed.
It is NOT compulsory to post original problems. But make sure it has not been posted on Brilliant.
Your question must have a polynomial. it can be like or . Both are allowed as long as the simplified form is a polynomial.
Format your proofs as
SOLUTION TO PROBLEM n
ask question relevant question here
To answer the latest question just shift to the "newest" mode
EDIT: for external discussion go to the discussion board