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a root of x^3-x-1=0 (IV Soros Olympiad 1997-98 R3 10.8)

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June 2, 2024
algebrapolynomial

Problem Statement

Let aa be the root of the equation x3−x−1=0x^3-x-1=0. Find an equation of the third degree with integer coefficients whose root is a3a^3.
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