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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  \[  3, 3^2=9\cong 3^2\equiv 9\  2, 3^3=3^2\cdot 3\cong 3^3\equiv 3^2\cdot 3\equiv  2\cdot 3=6 3\equiv 6  \]