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Unit pair pell parameter parity

Proved
D1Bound5.unit_pair_pell_parameter_parity

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

diophantine-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

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