lean_workbook_plus_65573

Disproved

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

Write $2^x = a$ , $5^x = b$ , $7^x = c$ . Equation becomes $a^4+b^4+c^4=abc(a+b+c)$ . $a$ , $b$ , $c$ are all positive real numbers, so by Muirhead's Inequality, $a^4+b^4+c^4=abc(a+b+c) \iff a=b=c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_65573 : ∀ a b c x : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → a^4 + b^4 + c^4 = a * b * c * (a + b + c) ↔ a = b ∧ b = c ∧ c = x   :=  by sorry

Source

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

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