Squarefree trace one discriminant
ProvedD1Bound5.squarefree_trace_one_discriminantdiophantine-tuplesnumber-theory
A trace-one coordinate model for a full imaginary quadratic integer ring has squarefree absolute discriminant.
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_one_discriminant {nu : ℤ}
(e : QuadInt 1 nu ≃+* 𝓞 K) (hd : 0 < QuadInt.discriminant 1 nu) :
Squarefree (QuadInt.discriminant 1 nu) := by sorry
end D1Bound5
end
Source
D1Bound5/MaximalCoordinates.lean, lines 74-99, SHA-256 db32306018b4cc9c601d0bd15648a6675ec234d51750d3dd04f9988129483527. Project: https://github.com/tomislav-math/d1-bound5-lean