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Composite_Number_has_Two_Divisors_Less_Than_It

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

divisorsproofwiki

A composite number greater than 1 can be expressed as the product of two positive integers strictly between 1 and n.

Preamble
import Mathlib.Data.Nat.Prime.Basic
Formal statement
theorem Composite_Number_has_Two_Divisors_Less_Than_It (n : ℕ) (hn : 1 < n) (hnp : ¬Nat.Prime n) : ∃ a b : ℕ, 1 < a ∧ a < n ∧ 1 < b ∧ b < n ∧ n = a * b := by sorry
Source
https://proofwiki.org/wiki/Composite_Number_has_Two_Divisors_Less_Than_It

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