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Erdős problem 509

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Let f(z)∈C[z]f(z) ∈ ℂ[z] be a monic non-constant polynomial. Can the set {z∈C:∣f(z)∣≤1}\{z ∈ ℂ : |f(z)| ≤ 1\} be covered by a set of closed discs the sum of whose radii is ≤2≤ 2?

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FormalConjectures/ErdosProblems/

509.lean

Retained formal statement2 of 5

Let f(z)∈C[z]f(z) ∈ ℂ[z] be a monic non-constant polynomial. Can the set {z∈C:∣f(z)∣≤1}\{z ∈ ℂ : |f(z)| ≤ 1\} be covered by a set of closed discs the sum of whose radii is ≤2≤ 2?

FormalConjectures/ErdosProblems/509.leanErdos509.erdos_5093 linesExact file
True ↔  ∀ (f : Polynomial ℂ),    f.Monic → f.natDegree ≠ 0 → ∃ ι, Nonempty (Erdos509.BoundedDiscCover {z | ‖Polynomial.eval z f‖ ≤ 1} 2 ι)
OpenStatement only, no proof