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Irreducible

Source: Iranian National Olympiad (3rd Round) 2007

August 28, 2007
number theory proposednumber theory

Problem Statement

Something related to this [url=http://www.mathlinks.ro/Forum/viewtopic.php?p=845756#845756]problem: Prove that for a set S⊂N S\subset\mathbb N, there exists a sequence \{a_{i}\}_{i \equal{} 0}^{\infty} in S S such that for each n n, \sum_{i \equal{} 0}^{n}a_{i}x^{i} is irreducible in Z[x] \mathbb Z[x] if and only if ∣S∣≥2 |S|\geq2. By Omid Hatami
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