Source labels openChecked July 26, 2026

Kummer–Vandiver conjecture

Kummer–Vandiver conjecture states that for every prime $p$ , the class number of the maximal real subfield of $\mathbb{Q}(\zeta_p)$ is not divisible by $p$ . -

Number theory AMS 11

Mathematical statement

Kummer–Vandiver conjecture states that for every prime $p$ , the class number of the maximal real subfield of $\mathbb{Q}(\zeta_p)$ is not divisible by $p$ .

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

kummer_vandiver

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem kummer_vandiver (p : ℕ+) (hp : p.Prime) :    ¬ ↑p ∣ (classNumber (maximalRealSubfield (CyclotomicField p ℚ))) := 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 sourceformalization Wikipediabackground

Kummer–Vandiver conjecture states that for every prime ppp, the class number of the maximal real subfield of Q(ζp)\mathbb{Q}(\zeta_p)Q(ζp​) is not divisible by ppp.

Statement artifacts, not proofs

kummer_vandiver

Kummer–Vandiver conjecture states that for every prime $p$ , the class number of the maximal real subfield of $\mathbb{Q}(\zeta_p)$ is not divisible by $p$ .