Show that the equation n!=a_1!a_2!···a_k!, with n−1 > a_1 ≥ a_2 ≥ ··· ≥ a_k, has only finitely many solutions.

1{(n, a, b) | n.factorial = a.factorial * b.factorial ∧ 1 < n ∧ 1 < a ∧ 1 < b ∧ b ≤ a ∧ a + 1 ≠ n} = {(10, 7, 6)}