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February 27th, 2011, 06:14 AM  #1 
Newbie Joined: Jan 2011 Posts: 4 Thanks: 0  How to prove that 3 is a generator of Zp, p = 17?
how to prove that 3 is a generator of Zp, and 2 is not a generator of Zp when p = 17? thanks 
February 27th, 2011, 11:36 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: How to prove that 3 is a generator of Zp, p = 17?
The order of 3 divides the order of the group, which is 17  1 = 16. If you show that the order of 3 is not 16/p for any prime p dividing 16 then you're done  the order must be 16 and so it generates the group. Since the only prime dividing 16 is 2, all you need to show is that 3^8 is not 1 mod 17.

February 27th, 2011, 08:03 PM  #3 
Newbie Joined: Jan 2011 Posts: 4 Thanks: 0  Re: How to prove that 3 is a generator of Zp, p = 17?
ok i get it, thanks!


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