lean_workbook_plus_69300

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Prove that there is no positive integers $x,y,z$ satisfying $x^2 y^4 - x^4 y^2 + 4x^2 y^2 z^2 +x^2 z^4 -y^2 z^4 =0$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_69300 : ¬∃ x y z : ℕ, x^2 * y^4 - x^4 * y^2 + 4 * x^2 * y^2 * z^2 + x^2 * z^4 - y^2 * z^4 = 0   :=  by sorry

Positive integer variables became unrestricted naturals, and ordinary polynomial subtraction became truncated subtraction.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

State nonexistence for x,y,z>0 in ℤ (or cast all natural inputs to ℤ before subtraction), retaining the exact polynomial equation.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.