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Complex Numbers z^720 - z^120 Real

2050SpecialistComplex NumbersNumber Theory

AIME I · 2018 · Problem 6

Let $N$ be the number of complex numbers $z$ with the properties that $|z|=1$ and $z^{6!}-z^{5!}$ is a real number. Find the remainder when $N$ is divided by $1000$. [[2018 AIME I Problems/Problem 6 | Solution]]
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