Prove2Me

lean_workbook_plus_72482

Proved

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

We have x2≡0,1(mod3)x^2 \equiv 0,1 \pmod{3} .\n\nTwo cases:\n+ If x2,y2,z2x^2,y^2,z^2 are divisible by 33 , then x=y=z=0x=y=z=0 .\n+ If x2≡1(mod3),  y2≡1(mod3),  z2≡1(mod3)x^2 \equiv 1 \pmod{3}, \; y^2 \equiv 1 \pmod{3}, \; z^2 \equiv 1 \pmod{3} . I don't know how to solve this cases.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_72482  (x y z : ℤ)
  (h₀ : x^2 ≡ 0 [ZMOD 3])
  (h₁ : y^2 ≡ 0 [ZMOD 3])
  (h₂ : z^2 ≡ 0 [ZMOD 3])
  (h₃ : x^2 + y^2 + z^2 = 0) :
  x = 0 ∧ y = 0 ∧ z = 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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