IMO Shortlist 1989 problem 5
Dodao/la:
arhiva2. travnja 2012. Find the roots
![r_i \in \mathbb{R}](/media/m/5/f/4/5f4f2d11e04483073cc8340320bcddee.png)
of the polynomial
![p(x) = x^n + n \cdot x^{n-1} + a_2 \cdot x^{n-2} + \ldots + a_n](/media/m/0/8/7/0876a51533edc6565f4bc1bbd476a904.png)
satisfying
%V0
Find the roots $r_i \in \mathbb{R}$ of the polynomial $$p(x) = x^n + n \cdot x^{n-1} + a_2 \cdot x^{n-2} + \ldots + a_n$$ satisfying $$\sum^{16}_{k=1} r^{16}_k = n.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1989