%hw0.tex: Homework assignment 13
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\centerline
{
\bf Dr. Z.'s Number Theory Homework assignment 13
}

{\bf 1.} Check empirically Wilson's theorem for (a) $n=3$ (b) $n=11$ (c) $n=23$

(Hint: do not compute $22!$, use modular arithmetic to find $22! \pmod {23}$)

{\bf 2.} Illustrate the proof of Wilson's theorem for $p=17$.

{\bf 3.} Check, empirically, Fermat's little theorem  for $p=31$, and $a=5$.

(Hint: do not compute $2^{23}$ and then divide by $23$ to get the remainder! Use modular arithmetic  modulo $31$)

{\bf 4.} Illustrate the Second proof of Fermat's little theorem with $p=7$ and $a=2$ .

{\bf 5.} How many necklaces of length $5$ are there with green, and blue beads? Write them all down.

{\bf 6.} How many necklaces of length $101$ are there with  $10$ colors?

{\bf 7.} Read, understand, and be able to reproduce (in a quiz or exam) the proof of Wilson's Theorem.

{\bf 8.} Read, understand, and be able to reproduce the three proofs of Fermat's little theorem.

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