Homework 4

This assignment is due by the beginning of class on Wednesday, September 24^{th}. Be sure to review the homework guidelines before getting started.

- Prove that for any prime number
*p*, the following congruence is valid:

\begin{align} 1^{p-1}+2^{p-1}+\cdots+(p-1)^{p-1} + p^{p-1} \equiv (p-1)! \mod{p}. \end{align}

- From Strayer, Chapter 2, do the following problems:
- 14
- 41(a)
- 42(d,f)
- 47
- 49
- 51(b,d)
- 55
- 60

It would also be good to get some practice on other problems, even though I won't be collecting them. There are loads of these problems in your book and elsewhere, so give some a shot.

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