One three three negative obstruction
ProvedD1Bound5.one_three_three_negative_obstructiondiophantine-tuplesnumber-theory
Three odd negative extensions cannot be pairwise compatible.
Preamble
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.Fintype.EquivFin 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.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
theorem _root_.D1Bound5.one_three_three_negative_obstruction (x y z r s t : ℤ)
(hx : x % 2 = 1) (hy : y % 2 = 1) (hz : z % 2 = 1)
(hr : x*y+1=r^2) (hs : x*z+1=s^2) (ht : y*z+1=t^2) : False := by sorry
end D1Bound5
end
Source
D1Bound5/OneThreeNegative.lean, lines 93-107, SHA-256 608590903d9651b83081c7c7b14962c497bd29944ae7411568eb23eee5734f08. Project: https://github.com/tomislav-math/d1-bound5-lean