lean_workbook_plus_9638

⚠️ 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.

Let $m$ be a positive odd integer, $m > 2.$ Find the smallest positive integer $n$ such that $2^{1989}$ divides $m^n - 1.$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_9638 (m : ℕ) (hm : 1 < m ∧ Odd m) : ∃ n : ℕ, (2^1989 ∣ m^n - 1 ∧ n >= 2^1988) ∧ (∀ k : ℕ, 2^1989 ∣ m^k - 1 → k >= n)   :=  by sorry

The accepted companion supplies the valuation-based corrected formula.

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

Proposed corrected statement

Minimize only over positive exponents. For K=1989 and odd m>2, put a=v₂(m−1),b=v₂(m+1): the least positive exponent is1 if K≤a, and2^max(1,K+1−a−b) otherwise. Remove the uniform false lower bound.

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.