Validity of coordinate square mask smallPairMask_0_2_13

Proved

D1Bound5.smallPairMask_0_2_13_valid

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

diophantine-tuplesnumber-theory

The mask smallPairMask_0_2_13 accepts every square modulo 43 in the quadratic coordinate algebra with relation ω² = τω − ν, where τ = 0 and ν = 2. This includes the zero square.

Preamble

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Data.Int.Sqrt
import Mathlib.Data.ZMod.Basic
import Mathlib.Tactic.Linarith
import Definitions.Def_D1Bound5_FastSquareTest_Definitions
import Definitions.Def_D1Bound5_SmallPairSieve_0_2_Definitions

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0









































theorem _root_.D1Bound5.smallPairMask_0_2_13_valid : CoordinateSquareMaskValid 0 2 42 smallPairMask_0_2_13 := by sorry






































end D1Bound5
end

Source

D1Bound5/SmallPairSieve_0_2.lean, lines 73-75, SHA-256 727515d7ea212c81f61f9fffb0286c4230effd65a8b39446d16d452557af244b. Project: https://github.com/tomislav-math/d1-bound5-lean

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