Problem

Source: Iranian National Olympiad (3rd Round) 2007

Tags: number theory proposed, number theory



Something related to this problem: Prove that for a set $ S\subset\mathbb N$, there exists a sequence $ \{a_{i}\}_{i = 0}^{\infty}$ in $ S$ such that for each $ n$, $ \sum_{i = 0}^{n}a_{i}x^{i}$ is irreducible in $ \mathbb Z[x]$ if and only if $ |S|\geq2$. By Omid Hatami