lean_workbook_plus_31297

Proved

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

Given the condition $a^2 + ab + b^2 \equiv 0 \pmod{p}$ , prove that $(a + b)^2 \equiv ab \pmod{p}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31297 (a b : ℤ) (p : ℕ) (hp : p.Prime) (h : a^2 + a*b + b^2 ≡ 0 [ZMOD p]) : (a + b)^2 ≡ a * b [ZMOD p]   :=  by sorry

Source