5

Part of 1989 IMO Shortlist

Problems(1)

Find roots satisfying power of 16 sum that equals n

Source: IMO Shortlist 1989, Problem 5, ILL 8

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.

algebrapolynomialrootsequationIMO ShortlistDiophantine equation