lean_workbook_plus_7976

⚠️ 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.

k is a positive integer not less than 4. Then for any positive integer s which is not bigger than $7^{k-1}$ we have $s^{2}+3$ can't be divided by $7^{k}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_7976 : ∀ k : ℕ, k >= 4 ∧ ∀ s : ℕ, s <= 7 ^ (k - 1) → s ^ 2 + 3 ≠ 0 ∧ ¬ 7 ^ k ∣ s ^ 2 + 3   :=  by sorry

The formalization has a quantifier/conjunction defect, while the accepted disproof deliberately refutes the same positive-range source claim.

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

Proposed corrected statement

Move k≥4 into an implication, but also replace the source’s false bound by an explicit counterexample statement k=4,s=306, where s²+3=39*7^4. A valid universal replacement bound is not known from this audit.

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.