so i got this question in a preparation test (http://prntscr.com/jmjs3r).I managed to show the last 2 questions but i got stuck getting a problem with the 1st one.
I started by doing {0,9,18,(18+9=27, so we get 6),15,(15+9=24, so we should(?) get 1?)} and then i stopped since i found a wrong number so the whole subgroup would be different.
Can someone explain where is mistake and why it doesn't work like that?
Thanks in advance!
$27 - 24 = 3; 27 = 24 + 3$ so $24 \equiv 3 \mod 24$. So you get $3$; not $6$.
$3+9 = 12$
$12 + 9 = 21$
$21 + 9 = 30$
$30 - 24 = 6; 30 = 24 + 6$ so $30 \equiv 6\mod 24$ so you get $6$.
$6+ 9 =15$
$15 + 9 = 24$
$24 - 24 = 0; 24 = 24 + 0$ so $24\equiv 0 \mod 24$ so you get $0$.
That is the entire group. It has $8$ elements.