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p(x) = 1 + x^n + x^{2n} product of 3 integer polynomial of degree >=1

Source: 2018 Swedish Mathematical Competition p6

May 1, 2021
algebrapolynomial

Problem Statement

For which positive integers nn can the polynomial p(x)=1+xn+x2np(x) = 1 + x^n + x^{2n} is written as a product of two polynomials with integer coefficients (of degree ≥1\ge 1)?
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