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irreducible in Z[x] iff irreducible in Q[x]

Source: 2023 Viet Nam math olympiad for high school students D2 P4

March 25, 2023
algebrapolynomial

Problem Statement

Prove that: a polynomial is irreducible in Z[x]\mathbb{Z}[x] if and only if it is irreducible in Q[x].\mathbb{Q}[x].
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