lean_workbook_plus_34113

⚠️ 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 for any distinct positive integers $x,y$ ,the number $x^4-x^2y^2+y^4$ is not a perfect square.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_34113 : ∀ x y : ℕ, x ≠ y ∧ 0 < x ∧ 0 < y → ¬ (∃ z : ℕ, x^4 - x^2*y^2 + y^4 = z^2)   :=  by sorry

The ordinary integer polynomial was evaluated using natural 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

For distinct positive integers x,y, place x⁴−x²y²+y⁴ inℤ before asserting it is not a square; verify the genuine Diophantine statement separately.

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.