Chapter 2.3, Problem 49E

(a)

To determine

To prove: If $p$ is a prime integer, then $p$ is a factor of $\left(\begin{array}{l}p\\ r\end{array}\right)$ for $r=1,2,\mathrm{\dots },p-1$.

(b)

To determine

To prove: If $p$ is a prime integer, the $p$ is a factor of $n^p-n$.