Erdős problem 509 · problems.science

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

Browse retained paths and inspect the exact material available for this Problem.

5 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

509.lean

Retained formal statement2 of 5

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 $≤ 2$ ?

FormalConjectures/ErdosProblems/509.leanErdos509.erdos_5093 linesExact file

1True ↔2  ∀ (f : Polynomial ℂ),3    f.Monic → f.natDegree ≠ 0 → ∃ ι, Nonempty (Erdos509.BoundedDiscCover {z | ‖Polynomial.eval z f‖ ≤ 1} 2 ι)

OpenStatement only, no proof

Sources

Search problems.science