Artin's conjecture in arithmetic progressions

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Let a,b,r∈Za,b,r\in\mathbb{Z} with gcd⁡(a,b)=1\gcd(a,b)=1, and suppose that r≠−1r\neq -1 and that rr is not a perfect mmth power for any m>1m>1. An integer rr is a primitive root modulo a prime qq when its powers represent all nonzero residue classes modulo qq. The strengthened Artin conjecture. There exist infinitely many primes qq in the arithmetic progression {a+kb}k∈Z\{a+kb\}_{k\in\mathbb{Z}} such that rr is a primitive root modulo qq. The source presents this as a stronger form of Artin's conjecture, beyond the infinitude assertion without a prescribed progression. It remains open in the source.

References

Primary source

Dave Witte Morris, “Some arithmetic groups that do not act on the circle”, arXiv:1210.3671 (2012).

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