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Covering a polynomial lemniscate by discs
Show that the set where a monic polynomial has modulus at most 1 can be covered by discs whose radii sum to at most 2.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "analysis" | |
| 5 | + ], | |
| 6 | + "type": "proof", | |
| 7 | + "source": { | |
| 8 | + "key": "erdos", | |
| 9 | + "name": "Erdős Problems", | |
| 10 | + "url": "https://www.erdosproblems.com/509", | |
| 11 | + "id": "509", | |
| 12 | + "curator": "Thomas Bloom", | |
| 13 | + "poser": "Paul Erdős", | |
| 14 | + "status": "open", | |
| 15 | + "as_of": "2026-10-20", | |
| 16 | + "catalog": "0521c19bbd38" | |
| 17 | + } | |
| 18 | +} | |