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(x-1)(x-2)(x-3)-1 is irreducible in Z[x]

Source: 2023 Viet Nam math olympiad for high school students D2 P1

March 25, 2023
algebra

Problem Statement

Prove that the polynomialP(x)=(x−1)(x−2)(x−3)−1P(x)=(x-1)(x-2)(x-3)-1is irreducible in Z[x].\mathbb{Z}[x].
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