| import Mathlib | |
| namespace OAI | |
| namespace Erdos970 | |
| namespace NumberTheoryLean.Targets | |
| open Filter | |
| open scoped Topology | |
| def IsJacobsthalBound (k m : ℕ) : Prop := | |
| ∀ n : ℕ, 0 < n → n.primeFactors.card ≤ k → | |
| ∀ a : ℤ, ∃ i : ℕ, i < m ∧ (a + i).natAbs.Coprime n | |
| def JacobsthalQuadratic : Prop := | |
| ∃ C : ℝ, 0 < C ∧ ∀ k : ℕ, 0 < k → | |
| ∃ m : ℕ, IsJacobsthalBound k m ∧ (m : ℝ) ≤ C * (k : ℝ) ^ 2 | |
| end NumberTheoryLean.Targets | |
| namespace Erdos970Final | |
| theorem erdos_970_quadratic : NumberTheoryLean.Targets.JacobsthalQuadratic := by | |
| sorry | |
| end Erdos970Final | |
| end Erdos970 | |
| end OAI | |