One three positive eight dvd
ProvedD1Bound5.one_three_positive_eight_dvddiophantine-tuplesnumber-theory
Positive rational common extensions of 1 and 3 are multiples of eight.
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_positive_eight_dvd {p r s : ℤ}
(hr : p+1=r^2) (hs : 3*p+1=s^2) : 8 ∣ p := by sorry
end D1Bound5
end
Source
D1Bound5/OneThreeNegative.lean, lines 71-82, SHA-256 608590903d9651b83081c7c7b14962c497bd29944ae7411568eb23eee5734f08. Project: https://github.com/tomislav-math/d1-bound5-lean