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Romania District MO 2022 Grade 10 P3

Source: Romania District MO 2022 Grade 10

March 28, 2022
complex numbersromaniaalgebra

Problem Statement

A positive integer n≥4n\geq 4 is called interesting if there exists a complex number zz such that ∣z∣=1|z|=1 and 1+z+z2+zn−1+zn=0.1+z+z^2+z^{n-1}+z^n=0. Find how many interesting numbers are smaller than 2022.2022.
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