# Dirichlet's Theorem on Arithmetic Progressions

1. Aug 2, 2011

### burritoloco

Hello,

I'm wondering if this is true, or if anyone has seen this before:

Let q, t be coprime integers. Then there exist infinitely many primes r such that
1. q is primitive root modulo r and
2. r = q + kt, for some k > 0.

If we take away 1, this becomes Dirichlet's Thm.

http://en.wikipedia.org/wiki/Dirichlet's_theorem_on_arithmetic_progressions

But could this be true when we allow 1 ?

Last edited: Aug 2, 2011
2. Aug 3, 2011

### Eynstone

The problem is definitely tougher than Dirichlet's Thm .!

3. Aug 4, 2011

### burritoloco

Haha, was just wondering if this had been done. It's definitely not in my analytic number theory book!

Last edited: Aug 4, 2011