AlphaEvolve problems·alphaevolve:20
Sendov's Conjecture
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For each $n \\geq 2$, let $C(n)$ be the smallest constant such that for any complex polynomial $f$ of degree $n \\geq 2$ with zeros $z_1, \\dots, z_n$ in the unit disk and critical points $w_1, \\dots, w_{n-1}$, $$ \\max_{1 \\leq k \\leq n} \\min_{1 \\leq j \\leq n-1} |z_k - w_j| \\leq C(n). $$ Sendov conjectured that $C(n)=1$.
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qed.bot, “Sendov's Conjecture”, https://qed.bot/t/alphaevolve-20, as of 30 Sep 2026.