Erdős problem 509

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

Sources

The source's own material, retained exactly.

5 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

509.lean

Retained formal statement1 of 5

FormalConjectures/ErdosProblems/509.leanErdos509.BoundedDiscCover.bound_nonneg_of_nonempty2 linesExact file

1∀ {M : Type u} [inst : MetricSpace M] (S : Set M),2  S.Nonempty → ∀ (r : ℝ) (ι : Type v) (bdc : Erdos509.BoundedDiscCover S r ι), 0 < r

APIStatement only, no proof