Erdős Problem #509
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
An \(r\)-bounded disc cover of a subset of a metric space \(M\) is an indexed family of closed discs whose radii sum to at most \(r\).
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 \(≤ 2\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/509.Prizenone
Topicsanalysis, polynomials
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/509
Attempts
submit one →Read our working report →
The live page status is OPEN, but it lists 1 claimed proof and current workers dhyantailor, benk, and Qing_Hong (accessed 2026-07-31).
SKIPPED