$\begingroup$

In preparation of a test, there were a few things in class that still confused me on how my instructor got the answer:

Using the following definition for $U_n$:

There were two examples we did in class that I don't understand clearly:

And this one:

Order of [3] in $U_{20}$ = 4

 [3]^2 = [9] [3]^3 = [7] [3]^4 = [1] [17] = [-3] = 4

I would really like to know what the process is behind these examples to understand them for my test next week. If possible, how would I start with finding the order of [7] in $U_{40}$?

Thanks for reading, really appreciate the help!

$\endgroup$ 5

1 Answer

$\begingroup$

Mod 40, we compute: 7*7 = 49 = 9, 7*7*7 = 343 = 23, 7*7*7*7 = 2401 = 1. Therefore the order of 7 is 4.

$\endgroup$ 1

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy