Dirichlet's Theorem on Arithmetic Progressions

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Dirichlet's Theorem on Arithmetic Progressions states that for any two coprime integers q and t, there are infinitely many primes r such that r can be expressed as r = q + kt for some integer k > 0. The discussion raises the question of whether this theorem can be extended to include the case where r = q + kt + 1, which complicates the problem beyond the original theorem. The participants agree that this extension is more challenging and not covered in standard analytic number theory literature.

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burritoloco
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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 ?
 
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The problem is definitely tougher than Dirichlet's Thm .!
 
Haha, was just wondering if this had been done. It's definitely not in my analytic number theory book!
 
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