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Which of the following statements are true? Select ALL that apply.

Let $p \geq 2$ be a prime. Then $p | (p - 1)!^2 + 2(p - 1)! + 1$.

Let $a$ be an integer and $p$ be a prime. Then $p | (a^p - a)^p$.

Let $n$ be composite. Then, $n | (n - 1)!$.

Let $a$ be an integer and $p$ be a prime. Then, $p | a^{p - 1} - 1$.