Artin's conjecture on primitive roots: Part Ii Power Squarefree Part Modeq One
Artin's Conjecture on Primitive Roots*, second half, power version If is a perfect power of a number whose squarefree part , then the density of the set of primes such that is a primitive root modulo ...
Mathematical statement
Artin's Conjecture on Primitive Roots*, second half, power version If is a perfect power of a number whose squarefree part , then the density of the set of primes such that is a primitive root modulo is given by
\left(1 - \prod_{p \mid \gcd(b_0, m)} \frac{1}{2 - p} \prod_{p \mid b_0, p\nmid m} \frac{1}{(1 + p - p ^ 2)}\right),$$ where $C$ is Artin's constant.Statement source: Wikipedia statement material
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Statement artifacts, not proofs
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Pinned Lean formulation 1
artin_primitive_roots.variants.part_ii_power_squarefreePart_modeq_one
theorem artin_primitive_roots.variants.part_ii_power_squarefreePart_modeq_one (a m b : ℕ) (ha : a = b ^ m) (hb : ∀ u v, 1 < u → b ≠ v ^ u) (hm₁ : 1 < m) (hm₂ : Odd m) (hb' : b.squarefreePart ≡ 1 [MOD 4]) : (S a).HasDensity (ArtinConstant * powCorrectionFactor m * entanglementFactor b m) {p | p.Prime} := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
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- Fidelity review
- Community formulation
References