Has Square Root Fast iff

Proved

D1Bound5.hasSquareRootFast_iff

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result hasSquareRootFast_iff in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

Preamble

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Data.Int.Sqrt
import Mathlib.Data.ZMod.Basic
import Mathlib.Tactic.Linarith
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_FastSquareTest_Definitions

Formal statement

section
namespace D1Bound5
open QuadInt



















theorem _root_.D1Bound5.hasSquareRootFast_iff {tau nu : ℤ}
    (hd : 0 < discriminant tau nu)
    (sieve : List (ℕ × ℕ)) (hvalid : CoordinateSquareSieveValid tau nu sieve)
    (z : QuadInt tau nu) : hasSquareRootFast sieve z = true ↔ ∃ r, r*r = z := by sorry

end D1Bound5
end

Source

D1Bound5/FastSquareTest.lean, lines 64-74, SHA-256 93fb33ff431ce54869bd6adeaf8ad3dbc69d1bda6af9b19b16adf05480dbef74. Project: https://github.com/tomislav-math/d1-bound5-lean

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