lean_workbook_plus_67306

⚠️ 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\n$f(n) = f(1)f(n - 1) + g(n - 1)$\n$g(n) = f(n - 1) g(n - 1)$\nf(1) = 2009\n$g(1) = 2009$\n\nFind $f(2009) + g(2009)$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_67306 (f g : ℕ → ℕ) (hf : ∀ n, f n = f 1 * f (n - 1) + g (n - 1)) (hg : ∀ n, g n = f (n - 1) * g (n - 1)) (hf1 : f 1 = 2009) (hg1 : g 1 = 2009) : f 2009 + g 2009 = 2009 ^ 2008   :=  by sorry

The predecessor recurrences were imposed at n=0 and1; natural truncation makes the initial data inconsistent. The fixed answer is not established for the genuine sequence.

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

Set f₁=g₁=2009 and impose f_n=f₁f_(n−1)+g_(n−1), g_n=f_(n−1)g_(n−1) only for n≥2. Determine f_2009+g_2009 for this well-defined sequence; do not retain the unverified answer2009^2008.

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.