lean_workbook_plus_25492

⚠️ 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.

Show that if a and b are positive integers, then $\left(a + \frac{1}{2}\right)^n + \left( b + \frac{1}{2}\right)^n$ is an integer for only finitely many positive integers $n$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_25492 (a b : ℤ) (ha : 0 < a) (hb : 0 < b) : {n : ℕ | (a + 1 / 2)^n + (b + 1 / 2)^n = ⌊(a + 1 / 2)^n + (b + 1 / 2)^n⌋}.Finite   :=  by sorry

Cast a,b to ℚ or ℝ before adding1/2, and express integrality by membership in the integer casts; retain a,b>0 and finiteness of positive exponents.

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

Proposed corrected statement

Cast a,b to ℚ or ℝ before adding1/2, and express integrality by membership in the integer casts; retain a,b>0 and finiteness of positive exponents.

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.