import Mathlib.Algebra.QuadraticDiscriminant
import Mathlib.Tactic

/-!
# Bulgarian Mathematical Olympiad 1998, Problem 6

Prove that the equation

     x²y² = z²(z² - x² - y²)

has no solutions in positive integers.

-/

namespace Bulgaria1998P6

theorem bulgaria1998_p6
    (x y z : ℤ)
    (hx : 0 < x)
    (hy : 0 < y)
    (_hz : 0 < z)
    (h : x^2 * y^2 = z^2 * (z^2 - x^2 - y^2)) :
    False := sorry

This problem does not yet have a complete solution.