Apply Wilson theory then $ n = p\in P$ $ (p - 1)! + 1 = p^k$ $ (p - 2)! = \frac {p^k - 1}{p - 1}$ Because $ p - 1|(p - 2)!$ so $ p - 1|\frac {p^k - 1}{p - 1}$ so $ p - 1|k$ Imply that $ k\geq p - 1$ So $ \frac {p^k - 1}{p - 1} > (p - 2)!$ tradition So it not true for $ n > 5$