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Squarefree trace zero parameter

Proved
D1Bound5.squarefree_trace_zero_parameter

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-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

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