# Math Help - prove there is no primitive root mod 3p

1. ## 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)

....

2. ## Re: prove there is no primitive root mod 3p

Is there a condition on p that is is prime?

3. ## Re: prove there is no primitive root mod 3p

yes, p is a prime

4. ## 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, $\phi(3p) = \phi(3)\phi(p) = 2(p-1)$

5. ## Re: prove there is no primitive root mod 3p

I solved this. thanks