lean_workbook_plus_58640

⚠️ 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.

$x^2$ can end with one of 0,1,4,5,6,9.\nBy little trial and error, we find that the possible pairs such that $x^2 + y^2$ ends with 0 are (0,0), (1,9), (4,6), (5,5), (6,4), and (9,1).

Why this node was retired

The posted statement is

theorem lean_workbook_plus_58640  (x y : ℕ)
  (h₀ : x^2 + y^2 < 20)
  (h₁ : x^2 + y^2 % 10 = 0) :
  (x,y) = (0,0) ∨ (x,y) = (1,9) ∨ (x,y) = (4,6) ∨ (x,y) = (5,5) ∨ (x,y) = (6,4) ∨ (x,y) = (9,1)   :=  by sorry

Modulo binds only y² in the target; the conclusion also confuses final square digits with the original numbers.

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

Assume (x²+y²)%10=0 and classify the pair of residues (x²%10,y²%10) as (0,0),(1,9),(4,6),(5,5),(6,4),(9,1). Remove the unrelated bound x²+y²<20.

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.