Question

I once collected six proofs of this theorem, for the field Z/p, and they can be found at http://www.math.uconn.edu/~kconrad/blurbs/grouptheory/cyclicFp.pdf. While Z/p is not the general finite field, since the intent of this MO question is to use proofs in a course to undergraduates without much background, surely Z/p is the only finite field that matters.