Source labels openChecked July 26, 2026

Artin's conjecture on primitive roots: Ii

Artin's Conjecture on Primitive Roots*, second half. Write $a = a_0 b^2$ where $a_0$ is squarefree. Under the conditions that $a$ is not a perfect power and $a_0\not\equiv 1\pmod{4}$ (sequence A85397 in the OEIS), the density of the set $S(a)$ of primes $...

Number theory AMS 11

Mathematical statement

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

artin_primitive_roots.parts.ii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem artin_primitive_roots.parts.ii    (a a_0 b : ℤ) (ha : a = a_0 * b ^ 2)    (ha' : ∀ n m, m ≠ 1 → a ≠ n ^ m) (ha_0 : Squarefree a_0)    (ha_0' : ¬a_0 ≡ 1 [ZMOD 4]) :    (S a).HasDensity ArtinConstant {p | p.Prime} := 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 A85397background LMS14background