Compfiles: Catalog Of Math Problems Formalized In Lean

CIIM2022P6


import Mathlib.Tactic

/-!
# Iberoamerican Interuniversity Mathematics Competition 2022, Problem 6

Given a positive integer m, let d(m) be the number of postive
divisors of m. Show that for every positive integer n, one
has
       d((n + 1)!) ≤ 2d(n!).
-/

namespace CIIM2022P6

def d : ℕ → ℕ
| m => (Nat.divisors m).card

theorem ciim2022_p6 (n : ℕ) (hn : 0 < n) :
    d (Nat.factorial (n + 1)) ≤ 2 * d (Nat.factorial n) := sorry

File author(s): David Renshaw

This problem does not yet have a complete formalized solution.

Open with the in-brower editor at live.lean-lang.org: