1. ## primitive root

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. ## Re: primitive root

p! = 7? How is that possible?

3. ## Re: primitive root

I wrote it in programming form.
I mean p is prime which not equal to 7.

4. ## Re: primitive root

do you have to prove that everything in the series is divided by "same" p?

5. ## Re: primitive root

the question is from old exam in Hebow and I understand it as "the same p"

6. ## Re: primitive root

Hi,
Here's a solution.

7. ## Re: primitive root

I was reviewing some of my posts, and realized what I said above is perfect nonsense. The method was correct, but it was all messed up. Here's a corrected version: