Let A(x) be a polynomial A_{0}
x^{n} + A_{1} X^{n-1}
+ ... + A_{n} with complex coefficients and
n distinct (complex) solutions z_{1},...,
z_{n}.
Also, let
Galois theory tells us that not for all The riddle: ## Part 1For which values of (n,m) is the sum of
B(z_{i}) (taken over all
z_{i}) calculable as a closed form function of
(A_{0}, ..., A_{n}, B_{0},
..., B_{m})?
## Part 2For which values of (n,m) is the product of
B(z_{i}) (taken over all
z_{i}) calculable as a closed form function of
(A_{0}, ..., A_{n}, B_{0},
..., B_{m})?
Answer both parts to be considered a solver. I thank Ito Kang for pointing this riddle out to me. Full credits for it will be given on the solution page. |
## List of solvers:Dan Dima (13 November 08:09) |

Elegant and original solutions can be submitted to
the puzzlemaster at __riddlesbrand.scso.com__.
Names of solvers will be posted on this page. Notify if you don't want
your name to be mentioned.

The solution will be published at the end of the month.

Enjoy!