Question 171
Given real numbers $a$, $b$, $c$ satisfying the condition: for each positive integer $n$, $a^n + b^n + c^n$ is an integer. Show that there exist integers $p$, $q$, $r$ such that $a$, $b$, $c$ are 3 solutions to the equation $x^3 + px^2 + qx + r = 0$.