Number Theory

Free Version
Difficult

NUMTH-Z9JVHP

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

A

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

B

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

C

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

D

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