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(x^2-1)^2(x^2-1)^2...(x^2-2023)^2+1 is irreducible

Source: 2023 Viet Nam math olympiad for high school students D2 P8

March 25, 2023
algebrapolynomial

Problem Statement

Prove that: for all positive integers n≥2,n\ge 2, the polynomial(x2−1)2(x2−1)2...(x2−2023)2+1(x^2-1)^2(x^2-1)^2...(x^2-2023)^2+1 is irreducible in Q[x].\mathbb{Q}[x].
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