lean_workbook_plus_12160

⚠️ 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 the equation $\frac{1}{x}+\frac{1}{y}=\frac{1}{N}$, find its solutions where $x, y$ are natural numbers and $N$ is a given natural number.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_12160 (N : ℕ) : { (x,y) : ℕ × ℕ | 1/x + 1/y = 1/N } =  { (x,y) : ℕ × ℕ | ∃ k : ℕ, x = k + 1 ∧ y = N * (k + 1) ∨ x = N * (k + 1) ∧ y = k + 1 }   :=  by sorry

Use rational reciprocals and require N,x,y>0. State the parametrization x=N+d,y=N+N²/d for positive divisors d∣N², allowing interchange of x,y.

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

Proposed corrected statement

Use rational reciprocals and require N,x,y>0. State the parametrization x=N+d,y=N+N²/d for positive divisors d∣N², allowing interchange of x,y.

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.