lean_workbook_plus_70898

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Rearrange the equation as follows: $z^{2}=(x^{2}+1)(y^{2}-1)+2006\Rightarrow x^{2}-y^{2}+z^{2}-x^{2}y^{2}=2005$ . Find solutions.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_70898 (x y z : ℤ) :  z^2 = (x^2 + 1) * (y^2 - 1) + 2006 ↔ x^2 - y^2 + z^2 - x^2 * y^2 = 2005   :=  by sorry

Source