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Jeremy Ting edited p7.tex
about 10 years ago
Commit id: bf16d61497b146b50e80697427fb60041e63a449
deletions | additions
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index 02241fe..53cd8b3 100644
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\item
Let n=5:
$4! \equiv -1\
(\textrm{mod}\ n)$ \textrm{mod}\ n$
$4! \equiv -1\
(\textrm{mod}\ 5)$ \textrm{mod}\ 5$
$4*3*2*1 \equiv -1\
(\textrm{mod}\ 5)$ \textrm{mod}\ 5$
$(4*1)(3*2) \equiv -1\
(\textrm{mod}\ 5)$ \textrm{mod}\ 5$
$(4*1) \equiv -1\
(\textrm{mod}\ 5)$ \textrm{mod}\ 5$
$(3*2) \equiv 1\
(\textrm{mod}\ 5)$ \textrm{mod}\ 5$
Then via Wilson's Theorem, it will then equal to $1\ \textrm{mod}\ 5$
\end{itemize}