lean_workbook_plus_53344

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Let ${a_{n}}$ be a sequence of integers, $a_{1}$ is odd, and for any positive integer $n$, we have $n(a_{n+1}-a_{n}+3)=a_{n+1}-a_{n}+3$, in addition, we have $2010$ divides $a_{2009}$. Find the smallest $n\ge 2$, so that $2010$ divides $a_{n}$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_53344 (a : ℕ → ℤ) (h1 : Odd (a 1)) (h2 : ∀ n, n * (a (n + 1) - a n + 3) = a (n + 1) - a n + 3) (h3 : 2010 ∣ a 2009) : ∃ n ≥ 2, 2010 ∣ a n   :=  by sorry

The target omits minimality and merely asks for an index already supplied in a hypothesis.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Require the witness n≥2 to be minimal: 2010∣a(n) and ∀m, 2≤m→2010∣a(m)→n≤m. Restrict the source recurrence to positive n.

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.