Generalizing Euler's Criterion

Euler's criterion - Wikipedia, the free encyclopedia

The way I think about Euler's Criterion is that the order of the group Z cross p is phi(p)=p-1 so we know that . Then also the only numbers which square to 1 are 1 and -1 so

My question is can we generalize this to different group?

Can we say:

Thanks!

Re: Generalizing Euler's Criterion

Since is an even number for all I think that answer is yes..

Re: Generalizing Euler's Criterion

Ah yes, because always includes a term, which of course if even.