lean_workbook_plus_34707

Disproved

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

Show that the equation $(x^2+y^2)^2-2(3x^2-5y^2)^2=z^2$ has no integer solutions.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_34707 : ¬ (∃ x y z : ℤ, (x^2 + y^2)^2 - 2 * (3 * x^2 - 5 * y^2)^2 = z^2)   :=  by sorry

Source