# Math Help - primitive root euler function

1. ## primitive root and euler function

(My English is not very well but I will try to explain myself as good as I can..)

I have 3 questions:

1. Assume 10 is a primitive root of p, a prime number , p!=7.
I need to prove that infinite number of this series :

31 331 3331 ...

is divided by p.

2.Prove that there is no natural number n such that n=2006* fi(n)
(when fi is euler function)

3. This is true that if a is primitive root af n, also is opposite? why?

Thanks!