Unit pair pell parameter parity
ProvedD1Bound5.unit_pair_pell_parameter_paritydiophantine-tuplesnumber-theory
A norm-two Pell solution has one of precisely the two relevant parameter congruences. No primitivity or positive-root assumption is used.
Preamble
import Lean.Elab.Tactic.Omega import Mathlib.Algebra.Group.Int.Units import Mathlib.Algebra.Polynomial.Monic import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Algebra.Squarefree.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Data.Finset.Card import Mathlib.Data.Int.GCD import Mathlib.Data.Int.Sqrt import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.GCongr import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Ring
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
theorem _root_.D1Bound5.unit_pair_pell_parameter_parity (d u v : ℤ)
(h : u ^ 2 - d * v ^ 2 = 2) : d % 8 = 7 ∨ d % 4 = 2 := by sorry
end D1Bound5
end
Source
D1Bound5/UnitPairPellParity.lean, lines 15-25, SHA-256 c3ad7f99dff414563641d91e1befe6673fc12f66d324008fa09e8f3018431ad6. Project: https://github.com/tomislav-math/d1-bound5-lean