lean_workbook_plus_63456

Proved

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

Prove that $\frac{a^5+b^5+c^5}{5}=\frac{a^3+b^3+c^3}{3}.\frac{a^2+b^2+c^2}{2}$ given $a+b+c=0$ and $a^3+b^3+c^3=3abc$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_63456 (a b c : ℝ) (h₁ : a + b + c = 0) (h₂ : a ^ 3 + b ^ 3 + c ^ 3 = 3 * a * b * c) : (a ^ 5 + b ^ 5 + c ^ 5) / 5 = (a ^ 3 + b ^ 3 + c ^ 3) / 3 * (a ^ 2 + b ^ 2 + c ^ 2) / 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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