Squarefree trace zero parameter
ProvedD1Bound5.squarefree_trace_zero_parameterdiophantine-tuplesnumber-theory
A trace-zero coordinate model for a full imaginary quadratic integer ring has squarefree nu.
Preamble
import Mathlib.Algebra.Polynomial.Monic import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Squarefree.Basic import Mathlib.Data.Int.GCD import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_Coordinates_Definitions
Formal statement
section
open scoped NumberField
open Module Polynomial
namespace D1Bound5
variable {K : Type*} [Field K]
variable [NumberField K]
theorem _root_.D1Bound5.squarefree_trace_zero_parameter {nu : ℤ}
(e : QuadInt 0 nu ≃+* 𝓞 K) (hd : 0 < QuadInt.discriminant 0 nu) : Squarefree nu := by sorry
end D1Bound5
end
Source
D1Bound5/MaximalCoordinates.lean, lines 57-72, SHA-256 db32306018b4cc9c601d0bd15648a6675ec234d51750d3dd04f9988129483527. Project: https://github.com/tomislav-math/d1-bound5-lean