Artin's conjecture in arithmetic progressions
Let with , and suppose that and that is not a perfect th power for any . An integer is a primitive root modulo a prime when its powers represent all nonzero residue classes modulo . The strengthened Artin conjecture. There exist infinitely many primes in the arithmetic progression such that is a primitive root modulo . 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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