lean_workbook_plus_23930

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

We can use Sonnhard's expression (which is equivalent to the given) to find all ordered pairs. Note that $2010$ only has $1$ perfect square factor, $1$ . Thus $(a-1)^2=1$ or $a=0, 2$ . However $a=0$ makes the given equation undefined, so only $a=2$ . We find $b=2012$ . We can check $(2, 2012)$ works.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_23930  (a b : ℤ)
  (h₀ : 0 < a ∧ 0 < b)
  (h₁ : (a - 1)^2 = 1)
  (h₂ : b^2 = 2010 * (a - 1)^2)
  (h₃ : 0 < a ∧ 0 < b) :
  a = 2 ∧ b = 2012   :=  by sorry

The asserted square relation gives b²=2010, impossible over integers, and it is incompatible with the excerpt’s b=2012. The excerpt omits the original equation.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Recover the original equation that produced the pair (2,2012); do not retain b²=2010(a−1)². A valid standalone theorem for the present relations is that no positive integer pair satisfies (a−1)²=1 and b²=2010(a−1)².

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.