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MathNet 2019-part-02 — 184 problems (EN–VI) Question 85

Math Olympiad Vault · MathNet 2019-part-02 — 184 problems (EN–VI)

Question 85

Find all complex numbers $a$ such that all coefficients of
$$
P(x) = (x - a)(x - a^2)(x - a^3)
$$
are real numbers.
(Matko Ljulj)