Problem

Source: Iranian National Olympiad (3rd Round) 2008

Tags: algebra, polynomial, algebra proposed



Suppose that $ f(x)\in\mathbb Z[x]$ be an irreducible polynomial. It is known that $ f$ has a root of norm larger than $ \frac32$. Prove that if $ \alpha$ is a root of $ f$ then $ f(\alpha^3+1)\neq0$.