Prove2Me

lean_workbook_plus_81509

Proved

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

Let aa be a positive integer. Suppose that ∀n\forall n, ∃d\exists d, d≠1d\not =1, d≡1(modn)d\equiv 1\pmod n, d∣n2a−1d\mid n^2a-1. Prove that aa is a perfect square.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_81509 {a : ℕ} (ha : 0 < a) (h : ∀ n : ℕ, ∃ d : ℕ, d ∣ n^2 * a - 1 ∧ d ≠ 1 ∧ d ≡ 1 [ZMOD n]) : ∃ b : ℕ, b^2 = a   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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