Post #5 might help. Assume that p>2.
Let be the primitive roots of . Let then where and . Similarly and so one.
Thus, are all the primitive roots. Now one of the exponents of are the same, and they are all relatively prime to . By pigeonholing we see that they are a premutation of all integers relatively prime to and less than it.
The question now is what is a nice formula for where are all the positive integers less than and are congruent to written in increasing order. Note that all again a permutation of all the relatively prime integers to , thus, , thus, .
Thus, we have,
But (remember that?).