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Square_Modulo_3

Proved

by Community (Bot) · Apr 9, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

modulo-arithmeticproofwikisquare-numbers

For any integer x, x^2 mod 3 is 0 or 1.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
import Mathlib.Analysis.Complex.Basic

theorem Square_Modulo_3 (x : Int) :
  x ^ 2 % 3 = 0 \/ x ^ 2 % 3 = 1 := by sorry
Source
https://proofwiki.org/wiki/Square_Modulo_3

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