lean_workbook_plus_82276

⚠️ 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.

This is old problem \nNote that the problem is equivalent to \nFind all $f:\mathbb{R} \rightarrow \mathbb{R}$ such that $f(f(x)+y)=f(x^2-y)+4f(x)y$ for all $x,y \in \mathbb{R}$ \nWhich is Iran TST $1996$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_82276 : ∀ f : ℝ → ℝ, (∀ x y, f (f x + y) = f (x^2 - y) + 4 * f x * y) ↔ ∃ k:ℝ, ∀ x, f x = k * x   :=  by sorry

The inserted linear classification is refuted by f(x)=x², which satisfies the source equation.

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 mathematical task without the inserted answer: This is old problem \nNote that the problem is equivalent to \nFind all $f:\mathbb{R} \rightarrow \mathbb{R}$ such that $f(f(x)+y)=f(x^2-y)+4f(x)y$ for all $x,y \in \mathbb{R}$ \nWhich is Iran TST $1996$ Require both necessity and sufficiency for a find-all/classification task; no replacement fixed answer is asserted in this audit.

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.