Thread: Find order of each element

1. Find order of each element

$\text{Find order of each element, find the generator ($\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 ???

2. Re: Find order of each element

Originally Posted by bigwave
$\text{Find order of each element, find the generator ($\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.

3. Re: Find order of each element

this was the note I tried to copy

yeah not sure the about the notation its probably just the ussual
the * might an x and q a 9

probably I just need to know what to look for.

I spent an hour surfing the net but...

4. Re: Find order of each element

Originally Posted by bigwave
$\text{Find order of each element, find the generator ($\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 ???
Originally Posted by bigwave

this was the note I tried to copy yeah not sure the about the notation its probably just the ussual
the * might an x and q a 9
probably I just need to know what to look for.
Well $q=9$ makes a hell of a lot more sense!

As always $\mathscr{O}{(1)}=1$
$\mathscr{O}{(2)}=6$ because $2^6\equiv 1\mod(9)$

Now you show us the rest: $\mathscr{O}{(4)}=?$, $\mathscr{O}{(5)}=?$, $\mathscr{O}{(7)}=?$, $\mathscr{O}{(8)}=?$,

5. Re: Find order of each element

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.