Validity of coordinate square mask smallPairMask_1_6_10

Proved

D1Bound5.smallPairMask_1_6_10_valid

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

diophantine-tuplesnumber-theory

The mask smallPairMask_1_6_10 accepts every square modulo 31 in the quadratic coordinate algebra with relation ω² = τω − ν, where τ = 1 and ν = 6. 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_1_6_Definitions

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0
































theorem _root_.D1Bound5.smallPairMask_1_6_10_valid : CoordinateSquareMaskValid 1 6 30 smallPairMask_1_6_10 := by sorry















































end D1Bound5
end

Source

D1Bound5/SmallPairSieve_1_6.lean, lines 58-60, SHA-256 a0d4837d188b69add6b5ce02fdb6e201af10251d67a713e6326c08a226549d2d. Project: https://github.com/tomislav-math/d1-bound5-lean

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