lean_workbook_plus_41360

Proved

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

If $a + b + c = 0$ , then $a^3b + b^3c + c^3a = -(a^2 + ab + b^2)^2$ is the negative of a square.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41360 {a b c : ℤ} (h : a + b + c = 0) :
    a^3 * b + b^3 * c + c^3 * a = -(a^2 + a * b + b^2)^2   :=  by sorry

Source