What is the most motivating way to introduce primitive roots

[matqkks]

I am teaching elementary number theory to first year undergraduate students. How do introduce the order of an integer modulo n and primitive roots? How do I make this a motivating topic and are there any applications of this area? I am looking at something which will have an impact.

 

[fresh_42]

I'm not sure whether this is motivating or not, because motivation depends a lot on personal views. An example could be the discrete Fourier transformation, or IIRC algorithms to breach an RSA coding, i.e. factorizing algorithms, or encryption in general.