IMO 1989 - Shortlist problems Question 5

(COL 1) Consider the polynomial $p(x)=x^n+nx^{n-1}+a_2x^{n-2}+\cdots+a_n$ having all real roots. If $r_1^{16}+r_2^{16}+\cdots+r_n^{16}=n$, where the $r_j$ are the roots of $p(x)$, find all such roots.