lean_workbook_plus_77198

⚠️ 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.

Given that $a$ and $b$ are coprime integers, and $a^{n-1} + b^{n-1}$ is divisible by $n$ where $a, b, n > 1$ and $n$ is odd. Prove that $2$ divides $n$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_77198 {a b n : ℤ} (h₁ : a > 1 ∧ b > 1 ∧ n > 1) (h₂ : Odd n) (h₃ : a + b = n) (h₄ : Nat.Coprime a.natAbs b.natAbs) : 2 ∣ n   :=  by sorry

The divisibility hypothesis a^(n−1)+b^(n−1)≡0 modn was replaced by a+b=n; the latter admits(2,3,5).

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

Proposed corrected statement

Restore the stated power-sum divisibility with a,b,n>1, odd n and gcd(a,b)=1. Clarify from the full source whether a+b=n was an additional hypothesis, and re-evaluate the contradiction claim; the current excerpt does not establish that every such odd n is impossible.

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.