A prime $p$ is an integer $\geq 2$ whose only positive integer factors are 1 and $p$.
(a) For any prime $p$ the number $p ^ { 2 } - p$ is always divisible by 3.\\
(b) For any prime $p > 3$ exactly one of the numbers $p - 1$ and $p + 1$ is divisible by 6.\\
(c) For any prime $p > 3$ the number $p ^ { 2 } - 1$ is divisible by 24.\\
(d) For any prime $p > 3$ one of the three numbers $p + 1 , p + 3$ and $p + 5$ is divisible by 8.