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irreducibility of a polynomial

Source: VJIMC 2022 2.2

April 11, 2022
algebrapolynomial

Problem Statement

For any given pair of positive integers m>nm>n find all a∈Ra\in\mathbb R for which the polynomial xm−axn+1x^m-ax^n+1 can be expressed as a quotient of two nonzero polynomials with real nonnegative coefficients.
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