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0789dda | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | 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
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