find the order of the elements in the group <Z*_{21}, .>
i think number of element in it is 20 from {1,2,3...20}
is it the divisors of 21 or divisors of 20?
please give an idea.
thank you.
The order of an element is the least positive integer such that . In the case of , we have . So with , we clearly have . With , we want . So ask yourself- . Solving for , and . So we get .
So does that help give you some intuition in solving for the orders of the other elements?