My Math Forum How to prove that 3 is a generator of Zp, p = 17?

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 February 27th, 2011, 05:14 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, 10:36 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, 07:03 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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### what are generators of Zp for p=17

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