Mathegoras

Complex numbers › Roots of unity and complex roots › Counting complex solutions

Largest finite count of small elements

University · ●●●●○ 100 pts

SS is a set of complex numbers such that if u,v∈Su, v \in S, then uv∈Suv \in S and u2+v2∈Su^{2}+v^{2} \in S. Suppose that the number NN of elements of SS with absolute value at most 11 is finite. What is the largest possible value of NN?

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roots of unityoptimizationcube roots of unity