MathNet 2009-part-03 — 175 problems (EN–VI) Question 86

Let $p$ be a prime number. Let $a$, $b$, and $c$ be integers that are divisible by $p$ such that the equation $x^{3} + a x^{2} + b x + c = 0$ has at least two different integer roots. Prove that $c$ is divisible by $p^{3}$.