Pell norm two coprime

Proved

D1Bound5.pell_norm_two_coprime

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

diophantine-tuplesnumber-theory

Auxiliary result pell_norm_two_coprime 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.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

Formal statement

section
namespace D1Bound5

















theorem _root_.D1Bound5.pell_norm_two_coprime {d x y : ℤ} (hx : 0 < x)
    (heq : x^2-d*y^2=2) : IsCoprime x y := by sorry





end D1Bound5
end

Source

D1Bound5/PellConvergentCompleteness.lean, lines 97-117, SHA-256 c43074daa228222fbe1ca798070304a8be11d05710c382ec9a9e73d7799c8266. Project: https://github.com/tomislav-math/d1-bound5-lean

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