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No nth- roots of rationals

Source: Brazil Math Olympiad 1995

March 16, 2006
algebrapolynomialcalculusintegrationgroup theoryabstract algebraGalois Theory

Problem Statement

Show that no one nn-th root of a rational (for nn a positive integer) can be a root of the polynomial x5−x4−4x3+4x2+2x^5 - x^4 - 4x^3 + 4x^2 + 2.
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