Small negative radicand not square
ProvedD1Bound5.small_negative_radicand_not_squarediophantine-tuplesnumber-theory
The two negative rational radicands are excluded uniformly beyond Δ=32.
Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Complex.Norm import Mathlib.Data.Fin.Tuple.Sort import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Fintype.EquivFin import Mathlib.Data.Int.GCD import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_Coordinates_Definitions
Formal statement
section
namespace D1Bound5
open QuadInt
theorem _root_.D1Bound5.small_negative_radicand_not_square {tau nu m : ℤ}
(hlarge : 32 < discriminant tau nu) (hm : m = -1 ∨ m = -3) :
¬ ∃ r : QuadInt tau nu, r*r = (m : QuadInt tau nu) := by sorry
end D1Bound5
end
Source
D1Bound5/SmallPairLargeDiscriminant.lean, lines 20-31, SHA-256 c69437fd6732a6665be073a5675405812d333a1b31dbbd565010be6a462d9850. Project: https://github.com/tomislav-math/d1-bound5-lean