Homework 4

This assignment is due by the beginning of class on Wednesday, September 24th. 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.

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