lean_workbook_plus_39449

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

If such numbers are $x,y$ , then $xy={k(k+1)\over 2}-x-y\iff (x+1)(y+1)={k(k+1)\over 2}+1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_39449 (x y k : ℤ) : (x * y = k * (k + 1) / 2 - x - y) ↔ (x + 1) * (y + 1) = k * (k + 1) / 2 + 1   :=  by sorry

Source