Quad Int — has Square Root iff
ProvedD1Bound5.QuadInt.hasSquareRoot_iffdiophantine-tuplesnumber-theory
The checker is necessary and sufficient, not merely a source of positive witnesses or a one-sided modular obstruction.
Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Data.Int.Sqrt import Mathlib.Tactic.Linarith import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_SquareTest_Definitions
Formal statement
section
namespace D1Bound5.QuadInt
variable {tau nu : ℤ}
theorem _root_.D1Bound5.QuadInt.hasSquareRoot_iff (hd : 0 < discriminant tau nu) (z : QuadInt tau nu) :
hasSquareRoot z = true ↔ ∃ r : QuadInt tau nu, r*r = z := by sorry
end D1Bound5.QuadInt
end
Source
D1Bound5/SquareTest.lean, lines 117-130, SHA-256 adcc13a33378056841f44d21785e69909232e4def68eb73ca742e5a49ce15ac3. Project: https://github.com/tomislav-math/d1-bound5-lean