lean_workbook_plus_27482

⚠️ 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 all sequence $a_1,a_2,a_3,\dots$ of positive integers such that $(n^2+1)a_{n+1}-a_n=n^3+n^2+1$ for all positive integer $n$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_27482 (a : ℕ → ℕ) (h : ∀ n : ℕ, (n^2+1)*a (n+1) - a n = n^3 + n^2 + 1) : a = fun n : ℕ => n^2 + 1   :=  by sorry

Replace the answer a(n)=n²+1 by a(n)=n for n≥1, and state positivity and the recurrence at positive indices as in the source. The additional posted index-zero equation determines a(0)=0.

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

Proposed corrected statement

Replace the answer a(n)=n²+1 by a(n)=n for n≥1, and state positivity and the recurrence at positive indices as in the source. The additional posted index-zero equation determines a(0)=0.

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.