lean_workbook_plus_47270

⚠️ 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 $n>3$ be a positive integer. $(a_{1},a_{2},a_{3},\ldots,a_{n})$ is a permutation of $(1,2,3,\ldots,n)$ . Prove that there exists some integer pair $(k,\ell)$ such that $k>\ell$ and $n \mid ka_{k}-\ell a_{\ell}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_47270 (n : ℕ) (hn : 3 < n) (a : ℕ → ℕ) (ha : Function.Bijective a) : ∃ k l : ℕ, k > l ∧ n ∣ k * a k - l * a l   :=  by sorry

The finite permutation and positive in-range indices become a bijection of ℕ and unrestricted natural indices.

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

Represent a as a permutation of {1,...,n}; require 1≤ℓ<k≤n and divisibility of the integer ka(k)−ℓa(ℓ), rather than unrestricted natural indices.

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.