Question 71
Let $p$ be an odd prime. Prove that the integer
$$
1! + 2! + 3! + \cdots + p! - \left\lfloor \frac{(p-1)!}{e} \right\rfloor
$$
is divisible by $p$.
$$
1! + 2! + 3! + \cdots + p! - \left\lfloor \frac{(p-1)!}{e} \right\rfloor
$$
is divisible by $p$.