$\text{Find order of each element, find the generator ($\delta$) of any properties}\\$
$\displaystyle \displaystyle Z_q^*=\left\{ 1,2,4,5,7,8\right\}
$
ok I just started this subject
is order the number of elements
but the question was ???
$\text{Find order of each element, find the generator ($\delta$) of any properties}\\$
$\displaystyle \displaystyle Z_q^*=\left\{ 1,2,4,5,7,8\right\}
$
ok I just started this subject
is order the number of elements
but the question was ???
I think that you must give much more of a context in which you find this question/
The notation $Z_q^*$ suggests this is a subset of a group in the integers with the operation multiplication$\mod(q)~?"$.
However, that guess really makes very little sense.
So please please give more context and/or definitions.
It is the multiplicative group of $\mathbb{Z}_9$.
$2^1\equiv 2 \pmod{9} $
$2^2\equiv 4 \pmod{9} $
$2^3\equiv 8 \pmod{9} $
$2^4\equiv 7 \pmod{9} $
$2^5\equiv 5 \pmod{9} $
$2^6\equiv 1 \pmod{9} $
The order of an element is the smallest positive integer power of the element that gives the identity element (1 in a multiplicative group). For 2 in this group, the smallest such power is 6.