Let p be a prime. If an integer g generates a subgroup of index t in (Z/pZ)*, then we say that g is a t-near primitive root modulo p. We point out the easy result that each coprime residue class contains a subset of primes p of positive natural density which do not have g as a t-near primitive root and we prove a more difficult variant.
- primitive root
- near-primitive root
- Artin's primitive root conjecture
- arithmetic progression
- secondary 11N69
- 2010 Mathematics subject classification
- primary 11N13