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WikipediaField theory and polynomials

Sendov's conjecture

Sendov's conjecture* states that for a polynomial f(z)=(z−r1)⋯(z−rn),(n≥2)f(z)=(z-r_{1})\cdots (z-r_{n}),\qquad (n\geq 2) with all roots r1,...,rnr_1, ..., r_n inside the closed unit disk ∣z∣≤1|z| ≤ 1, each of the nn roots is at a distance no more than 11 from at least one critical ...

Field theory and polynomialsAMS 12AMS 30AMS 52

Mathematical statement

Sendov's conjecture* states that for a polynomial f(z)=(z−r1)⋯(z−rn),(n≥2)f(z)=(z-r_{1})\cdots (z-r_{n}),\qquad (n\geq 2) with all roots r1,...,rnr_1, ..., r_n inside the closed unit disk ∣z∣≤1|z| ≤ 1, each of the nn roots is at a distance no more than 11 from at least one critical point.

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

sendov_conjecture

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem sendov_conjecture (n : ℕ) (hn : 2 ≤ n) : n.SatisfiesSendovConjecture := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References

Pinned Formal Conjectures sourceformalizationWikipediabackground