Hi. I need to: prove the group (Zp*,x) has exactly one element of order 2. Here, p is prime and (Zp*,x) is the set {1, 2,....., p-1} under multiplication modulo p. Any help would be much appreciated!
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If you do not know the previous. Then you might want to think about the polynomial [itex]X^2-1[/itex] in [itex]\mathbb{Z}_p[X][/itex]. What do you know about its roots??