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