lean_workbook_plus_71911

⚠️ 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.

For $y = \frac {x+z} {2}$ the equation becomes $33x^5 + 5x^4z + 10x^3z^2 + 10x^2z^3 + 5xz^4 - 31z^5 = 0$ . Now check divisibility by $x$ , respectively $z$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_71911 : ∀ x y z : ℂ, y = (x + z) / 2 → 33 * x ^ 5 + 5 * x ^ 4 * z + 10 * x ^ 3 * z ^ 2 + 10 * x ^ 2 * z ^ 3 + 5 * x * z ^ 4 - 31 * z ^ 5 = 0   :=  by sorry

The excerpt omits the original equation, so the inferred fifth-power premise requires source confirmation.

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

Proposed corrected statement

Restore the original equation in addition to y=(x+z)/2. If that equation is x^5+y^5=z^5, substitution gives exactly the displayed polynomial.

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.