Q:

9th power of any positive integer is of the form $19 m $ or $19 m \pm 1$

Which of the following statements are true? 

The 9th power of any positive integer is of the form $19 m $ or $19 m \pm 1$.
For any positive integer $n$, the number $n^{13} - n$ is divisible by
2730. 
The number $18!  + 1$ is divisible by 437. 

I am stuck on this problem.  Can anyone help me please...

A:

Hints: 

Euler's theorem: for $a$ and $n$ relatively prime, $a^{\varphi(n)}\equiv 1\bmod n$.
Wilson's theorem: for a prime number $p$, $(p-1)!\equiv -1\bmod p$.

