MathDB
Find roots satisfying power of 16 sum that equals n

Source: IMO Shortlist 1989, Problem 5, ILL 8

September 18, 2008
algebrapolynomialrootsequationIMO ShortlistDiophantine equation

Problem Statement

Find the roots riR r_i \in \mathbb{R} of the polynomial p(x) \equal{} x^n \plus{} n \cdot x^{n\minus{}1} \plus{} a_2 \cdot x^{n\minus{}2} \plus{} \ldots \plus{} a_n satisfying \sum^{16}_{k\equal{}1} r^{16}_k \equal{} n.