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:

(1)

\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.