AlphaEvolve problems·alphaevolve:45
Sum-product problems
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Given a natural number $N$ and a ring $R$ of size at least $N$, let $C(R, N)$ denote the least possible value of $\\max(|A+A|, |A \\cdot A|)$ where $A$ ranges over subsets of $R$ of cardinality $N$. Establish upper and lower bounds for $C(R, N)$ that are as strong as possible.
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qed.bot, “Sum-product problems”, https://qed.bot/t/alphaevolve-45, as of 30 Sep 2026.