lean_workbook_plus_47782

Disproved

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

Is there any $k$ such that there are no solutions to $ab + bc + ca = a + b + c + k$ ?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_47782 : ∃ k : ℤ, ¬ (∃ a b c : ℤ, a * b + b * c + c * a = a + b + c + k)   :=  by sorry

Source