lean_workbook_plus_49273

Proved

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

Let $x,y,z$ be integers such that $(x-y)^2+(y-z)^2+(z-x)^2 = xyz$ . Prove that $x^3+y^3+z^3$ is divisible by $x+y+z+6$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_49273 (x y z : ℤ) (h : (x - y) ^ 2 + (y - z) ^ 2 + (z - x) ^ 2 = x * y * z) : (x + y + z + 6) ∣ (x ^ 3 + y ^ 3 + z ^ 3)   :=  by sorry

Source

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

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