Problem

Source: Indonesia TST 2009 Second Stage Test 3 P1

Tags: algebra, polynomial, quadratics, number theory proposed, number theory



Find the smallest odd integer $ k$ such that: for every $ 3-$degree polynomials $ f$ with integer coefficients, if there exist $ k$ integer $ n$ such that $ |f(n)|$ is a prime number, then $ f$ is irreducible in $ \mathbb{Z}[n]$.