lean_workbook_plus_59695

Proved

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

Consider modulo $11.$ By Fermat's Little Theorem, for all $n$ not divisible by $11,$ $n^{10} \equiv 1 \pmod{11}.$ Thus, for all $n,$ either $n^{10} \equiv 0 \pmod{11}$ or $n^{10} \equiv 1 \pmod{11}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_59695 (n : ℕ) : (n ^ 10) % 11 = 0 ∨ (n ^ 10) % 11 = 1   :=  by sorry

Source

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

View graph