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com/papers/an-explicit-high-degree-threshold-for-sendovs-conjecture-deEGnk8R It seemed clear that a different strategy would be needed for proving Sendov
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A digestion of the proof of Sendov’s conjecture | What's new

https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/
If one ignores the errors, one can show that these conditions are only simultaneously feasible if and all the vanish, but the argument was somewhat subtle (I had to proceed by inspecting the second Fourier coefficient of (1))