lean_workbook_plus_7547

⚠️ 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 $a_1, a_2, \ldots, a_n$ be a sequence of real numbers. Suppose that for each positive integer $k$ , we have $(1+a_1^k)(1+a_2^k)\cdots (1+a_n^k) = 1$ . Prove that $a_1 = a_2 = \ldots = a_n = 0$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_7547 (n : ℕ) (a : Fin n → ℝ) (h : ∀ k : ℕ, ∏ i, (1 + (a i)^k) = 1) : ∀ i, a i = 0   :=  by sorry

The accepted proof uses k=0 to force an empty index type; this source-excluded case trivializes the claim.

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 product equality only for k≥1. Then use k=2 to conclude every aᵢ=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.