Pair Seed Candidate eq
ProvedD1Bound5.pairSeedCandidate_eqdiophantine-tuplesnumber-theory
Every actual extension is reconstructed from either chosen square root.
Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_PairExtensionCore_Definitions
Formal statement
section
namespace D1Bound5
open QuadInt
theorem _root_.D1Bound5.pairSeedCandidate_eq {tau nu : ℤ}
(hd : 0 < discriminant tau nu) (a z q : QuadInt tau nu)
(ha : a ≠ 0) (hq : q*q = a*z+1) : pairSeedCandidate a q = z := by sorry
end D1Bound5
end
Source
D1Bound5/PairExtensionCore.lean, lines 46-61, SHA-256 d45446b353f1adcd08c1943cfe73040bef48ad11485fc541c7388b34f9e5255f. Project: https://github.com/tomislav-math/d1-bound5-lean