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Irreducible sequence

Source: Iran TST 2007, Day 3

May 20, 2007
algebrapolynomialnumber theory proposednumber theory

Problem Statement

Does there exist a a sequence a0,a1,a2,…a_{0},a_{1},a_{2},\dots in N\mathbb N, such that for each i≠j,(ai,aj)=1i\neq j, (a_{i},a_{j})=1, and for each nn, the polynomial ∑i=0naixi\sum_{i=0}^{n}a_{i}x^{i} is irreducible in Z[x]\mathbb Z[x]? By Omid Hatami
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