AlphaEvolve problems·alphaevolve:60
The no 5 on a sphere problem
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For $n$ a natural number, let $C(n)$ denote the size of the largest subset of $[n]^3 = \\{1,\\dots,n\\}^3$ such that no 5 points lie on a sphere or a plane. Obtain upper and lower bounds for $C(n)$ that are as strong as possible.
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qed.bot, “The no 5 on a sphere problem”, https://qed.bot/t/alphaevolve-60, as of 30 Sep 2026.