prove there is no primitive root mod 3p

• March 27th 2013, 03:23 AM
userit8
prove there is no primitive root mod 3p
when p odd , p>3.

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I don't know how to cintinue:

a^(p-1)=1(modp)
a^2=1(mod3)

....
• March 27th 2013, 04:53 AM
Kanwar245
Re: prove there is no primitive root mod 3p
Is there a condition on p that is is prime?
• March 27th 2013, 05:21 AM
userit8
Re: prove there is no primitive root mod 3p
yes, p is a prime
• March 27th 2013, 05:39 AM
Kanwar245
Re: prove there is no primitive root mod 3p
Okay so this might help
Suppose a is a primitive root of $\{Z}_{3p}^X$

Also, $\phi(3p) = \phi(3)\phi(p) = 2(p-1)$
• March 27th 2013, 07:28 AM
userit8
Re: prove there is no primitive root mod 3p
I solved this. thanks