Liouville Function Problem

Let $\lambda (n)$ be the Liouville function. Prove that there exist infinitely many positive integers $n$ such that $\lambda (n) = \lambda (n+1) = \lambda (n+2)$.

Replace sorry in the template below with your solution. Mathlib version used by the checker is v4.29.0.

import Mathlib.Data.Nat.Factorization.Basic

def Ω (n : ℕ) : ℕ := (Nat.factorization n).sum (fun _ e => e)

def Liouville (n : ℕ) : ℤ := (-1) ^ (Ω n)

theorem solution : ∀ N, ∃ n ≥ N,
    Liouville n = Liouville (n + 1) ∧ Liouville n = Liouville (n + 2) := sorry

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