AlphaEvolve problems·alphaevolve:7
Difference Bases
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For any natural number $n$, let $\\Delta(n)$ be the size of the smallest set $B$ of integers such that every natural number from $1$ to $n$ is expressible as a difference of two elements of $B$ (such sets are known as difference bases for the interval $\\{1,\\dots,n\\}$). Write $C(n) \\coloneqq \\Delta^2(n)/n$, and $C \\coloneqq \\inf_{n \\geq 1} C(n)$. Establish upper and lower bounds on $C$ that are as strong as possible.
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qed.bot, “Difference Bases”, https://qed.bot/t/alphaevolve-7, as of 30 Sep 2026.