Integral of quadratic relation

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

section
open scoped NumberField
open Module Polynomial

namespace D1Bound5

variable {K : Type*} [Field K]


theorem _root_.D1Bound5.integral_of_quadratic_relation (a b : ℤ) {x : K}
    (h : x*x = (a : K)+(b : K)*x) : IsIntegral ℤ x := by sorry

variable [NumberField K]









end D1Bound5
end