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February 27th, 2011, 05:14 AM   #1
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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
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February 27th, 2011, 10:36 AM   #2
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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.
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February 27th, 2011, 07:03 PM   #3
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Re: How to prove that 3 is a generator of Zp, p = 17?

ok i get it, thanks!
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