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