Hi guys, I'm taking a course about cryptography, and Im currently confused on a topic I learned about. Basically my task is to find 5 generators by testing g=2,3,4,5,6,7. I dont quite understand what generators are but what I understand ( or think I understand) is that if I take p, which is the number of the modulus and observe p-1's factors, I then raise g to those powers and mod by p and see if I get one as an answer. If I get one, then I know the number is not a generator. Please help me understand this topic- the specific question is test g=2,3,4,5,6,7... for being generators mod 103 until you can find one of them. Since 102's factors are 2,3,17,51 and 6, I first tried testing 2 out. I did 2^2,2^3,2^17,2^51 and 2^6 and modded them all by 103 and didnt get a single 1. Does this mean that 2 is a generator? (I already know it is, but I want to know why). Thanks for any help, its appreciated, thanks.
EDIT: http://crypto.stanford.edu/pbc/notes/numbertheory/gen.xhtml this link may help explain