1. Nov 26, 2011 #1

   ae1709

   

   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!

    

   ae1709, Nov 26, 2011
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3. Nov 26, 2011 #2

   Office_Shredder

   

   Staff Emeritus

   Science Advisor

   Gold Member

   I think the easier half is: which element has order two?
   
   It might help if you write down the condition of what it means to have order 2

    

   Office_Shredder, Nov 26, 2011
4. Nov 26, 2011 #3

   micromass

   

   Insights Author

   Something that might help you is knowing that [itex]\mathbb{Z}_p^*[/itex] is cyclic. Do you know this already??

    

   micromass, Nov 26, 2011
5. Nov 26, 2011 #4

   micromass

   

   Insights Author

   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??

    

   micromass, Nov 26, 2011

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