lean_workbook_plus_82850

⚠️ 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.

This means that $p \mid 2013-1 \Rightarrow p=2 \text{ or } 503$ . Then, using Lifting The Exponent Lemma, one easily gets the desired solutions as $\boxed{(p,n)=(2,98) \text{ or } (503,99)}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_82850    (p : ℕ)
    (n : ℕ)
    (h₀ : 1 < p)
    (h₁ : 0 < n)
    (h₂ : (p^n - 1) ∣ 2013 - 1) :
    (p = 2 ∧ n = 98) ∨ (p = 503 ∧ n = 99)   :=  by sorry

The excerpt is a partial LTE solution; divisibility p^n−1∣2012 alone is a different problem and admits(2,1).

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 original prime and valuation equation that led to p∣2012 before asking for its solution pairs.

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.