lean_workbook_plus_61552

Disproved

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

Prove that $a^5+b^5+c^5 \ge \frac{1}{27} (a+b+c)^3 (a^2+b^2+c^2) \ge abc(a^2+b^2+c^2)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_61552 : ∀ a b c : ℝ, a ^ 5 + b ^ 5 + c ^ 5 ≥ (1 / 27) * (a + b + c) ^ 3 * (a ^ 2 + b ^ 2 + c ^ 2) ∧ (1 / 27) * (a + b + c) ^ 3 * (a ^ 2 + b ^ 2 + c ^ 2) >= a * b * c * (a ^ 2 + b ^ 2 + c ^ 2)   :=  by sorry

Source

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

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