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Finite geometric partial sums set size

2175ExpertPolynomialsComplex Numbers

Shortlisted Problems for the 64th NMO

For each complex $z$ define $A_z = \{1+z+z^2+\dots+z^n \mid n \in \mathbb{N}\}$. a) Find all $z$ for which $A_z$ is finite. b) How many complex numbers $z$ have the property that $A_z$ has 2013 elements?
0 students attempted0% solvedRating 2175

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