deletions | additions       diff --git a/friends.tex b/friends.tex  index 2e56eca..965bca8 100644  --- a/friends.tex  +++ b/friends.tex 
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Another particular fact about these fields, is that exist elements whose powers cover all the non-zero elements of thield itself. As an example consider the elements $3$ and $5$ in $\ZZ_7$.  The powers of $3$ are  \begin{align} \begin{align*}  3 \\ 3^2\equiv 9\equiv 2\\  3^3\equiv 3^2\cdot 3\equiv 2\cdot 3\equiv 6 \\  3^4\equiv 3^3\cdot 3\equiv 6\cdot 3\equiv 4 \\  3^5\equiv 3^4\cdot 3\equiv 4\cdot 3\equiv 5 \\  3^6\equiv 3^5\cdot 3\equiv 5\cdot 3\equiv 1   \end{align} \end{align*}  The powers of $5$ are  \begin{align} \begin{align*}  & 5 \\  & 5^2\equiv 25\equiv 4\\  & 5^3\equiv 5^2\cdot 5\equiv 4\cdot 5\equiv 6 \\  & 5^4\equiv 5^3\cdot 5\equiv 6\cdot 5\equiv 2 \\  & 5^5\equiv 5^4\cdot 5\equiv 2\cdot 5\equiv 3 \\  & 5^6\equiv 5^5\cdot 5\equiv 3\cdot 5\equiv 1   \end{align} \end{align*}