lean_workbook_plus_26184

⚠️ 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.

Any number can be either multiple of $p$ (a prime) or relatively prime with $p$ . The multiples of $p$ less than $p^k$ are $p, 2p,..., (p^{k-1}-1)p$ , in total there are $p^{k-1}-1$ . So there are $(p^k-1)-(p^{k-1}-1=p^k-p^{k-1}=p^{k-1}(p-1)$ numbers relatively prime with $p$ less than $p^k$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_26184 : ∀ k : ℕ, ∀ p : ℕ, p.Prime → (p^k-1) - (p^(k-1)-1) = p^(k-1)*(p-1)   :=  by sorry

Require k≥1, matching the source’s positive prime-power counting argument.

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

Proposed corrected statement

Require k≥1, matching the source’s positive prime-power counting argument.

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.