Exists root error three
ProvedD1Bound5.exists_root_error_threediophantine-tuplesnumber-theory
First-row entries in the A >= 1, B >= 3 determinant argument.
Preamble
import Mathlib.Analysis.Complex.Basic import Mathlib.Data.Complex.Basic import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Ring
Formal statement
section
namespace D1Bound5
theorem _root_.D1Bound5.exists_root_error_three (x t : ℂ)
(hx : 3 ≤ ‖x‖) (ht : t^2 = x*(x+1)) :
∃ v : ℂ, (v=t ∨ v=-t) ∧
‖v-x‖ < (5/9 : ℝ) ∧
‖(v-x)-(1/2 : ℂ)‖ < (25/486 : ℝ) := by sorry
end D1Bound5
end
Source
D1Bound5/RootErrorMagnitude.lean, lines 139-154, SHA-256 090472365e3db009e37be35676f898eae037822776991930233fc88ea690af2b. Project: https://github.com/tomislav-math/d1-bound5-lean