lean_workbook_plus_5036

⚠️ 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.

The smallest point with positive integer values for both x and y is when rearranging the equation, $y=\frac{17x-2}{23}$ . So $17x\equiv 2 \bmod{23}$ and $17x-2\equiv 0 \bmod{23}$ . The smallest integer values are $(15,11)$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_5036  (x y : ℕ)
  (h₀ : 0 < x ∧ 0 < y)
  (h₁ : (17 * x - 2) % 23 = 0)
  (h₂ : (17 * y - 2) % 23 = 0)
  (h₃ : ∀ x' y', (17 * x' - 2) % 23 = 0 ∧ (17 * y' - 2) % 23 = 0 → x' ≥ x ∧ y' ≥ y) :
  x = 15 ∧ y = 11   :=  by sorry

The target imposes unrelated congruences on both coordinates and includes the zero competitor via truncated subtraction, contradicting positivity.

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

Find the least positive integer pair satisfying 17x−23y=2, or y=(17x−2)/23 using exact division, and conclude (x,y)=(15,11). Restrict all minimality competitors to positive solutions of that same equation.

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.