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Omni-MATH / S is a set of complex numbers such that if u,v∈S, then uv∈S and u²+v²∈S. Suppose that the number N of elements of S with absolute value at most 1 is finite. What is the largest pos…

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problem

SS is a set of complex numbers such that if u,v∈Su, v \in S, then uv∈Su v \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 1 is finite. What is the largest possible value of NN ?
Plain-text mathematical notation (without MathML)
S is a set of complex numbers such that if u,v∈S, then uv∈S and u²+v²∈S. Suppose that the number N of elements of S with absolute value at most 1 is finite. What is the largest possible value of N ?
Original LaTeX notation
$S$ is a set of complex numbers such that if $u, v \in S$, then $u v \in S$ and $u^{2}+v^{2} \in S$. Suppose that the number $N$ of elements of $S$ with absolute value at most 1 is finite. What is the largest possible value of $N$ ?

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task_id
eb81ccce-6e7b-5713-b959-92e7b0e352b6
task_key
test--eb81ccce-6e7b-5713-b959-92e7b0e352b6
task_revision_id
1
config / split
/ test

Official source

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