Pell CFSolutions complete

Proved

D1Bound5.pellCFSolutions_complete

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

A finite checked continued-fraction computation contains every positive norm-two solution below its stopping numerator. The output list is the actual filtered trace of the integer algorithm.

Preamble

import Mathlib.Data.Rat.Lemmas
import Mathlib.NumberTheory.DiophantineApproximation.Basic
import Mathlib.NumberTheory.Real.Irrational
import Mathlib.RingTheory.Coprime.Lemmas
import Mathlib.RingTheory.Int.Basic
import Mathlib.Tactic
import Definitions.Def_D1Bound5_PellCFPrefixCheck_Definitions

Formal statement

section
namespace D1Bound5
















































theorem _root_.D1Bound5.pellCFSolutions_complete {d a0 X x y : ℤ} {N : ℕ}
    (hd : 7 ≤ d) (hcheck : pellCFPrefixCheck d a0 N = true)
    (hstop : X < (pellCFAt d a0 (pellCFInit a0) N).p)
    (hx : 0 < x) (hy : 0 < y) (heq : x^2-d*y^2=2) (hX : x ≤ X) :
    (x,y) ∈ pellCFSolutions d a0 X N := by sorry



end D1Bound5
end

Source

D1Bound5/PellCFPrefixCheck.lean, lines 274-294, SHA-256 a5468d17d5b8fd8febaae9f486b606a6148827a88a3b76dca5782d036662adba. Project: https://github.com/tomislav-math/d1-bound5-lean

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