lean_workbook_plus_37433

Proved

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

If $p$ is a prime so that $p\equiv 1 mod 4$ , then $x^2\equiv 1 \mod p$ if and only if $x\equiv \pm 1 \mod p$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_37433 (p : ℕ) (hp : p.Prime) (hp1 : p ≡ 1 [ZMOD 4]) : (∃ x : ZMod p, x^2 = 1) ↔ ∃ x : ZMod p, x = 1 ∨ x = -1   :=  by sorry

Source

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

View graph