lean_workbook_plus_17376

⚠️ 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.

Find $ax^5 + by^5$ if the real numbers $a,b,x,$ and $y$ satisfy the equations \begin{align*} ax + by &= 3, \ ax^2 + by^2 &= 7, \ ax^3 + by^3 &= 16, \ ax^4 + by^4 &= 42. \end{align*}

Why this node was retired

The posted statement is

theorem lean_workbook_plus_17376 (a b x y : ℝ) (h₁ : a * x + b * y = 3) (h₂ : a * x ^ 2 + b * y ^ 2 = 7) (h₃ : a * x ^ 3 + b * y ^ 3 = 16) (h₄ : a * x ^ 4 + b * y ^ 4 = 42) : a * x ^ 5 + b * y ^ 5 = 124   :=  by sorry

The source asks for all solutions or a value; the stored theorem supplies an unsupported answer contradicted by an accepted disproof.

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

Proposed corrected statement

Prove the fifth weighted moment is 20, using the recurrence M_{k+2}=−14M_{k+1}+38M_k derived from the four data.

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.