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Primes in arithmetic progressions and nonprimitive roots. (English) Zbl 1472.11031

Summary: Let \(p\) be a prime. If an integer \(g\) generates a subgroup of index \(t\) in \((\mathbb{Z}/p\mathbb{Z})^{\ast },\) 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.

MSC:

11A15 Power residues, reciprocity
11N13 Primes in congruence classes
11N69 Distribution of integers in special residue classes

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Full Text: DOI arXiv

Online Encyclopedia of Integer Sequences:

Genocchi irregular primes.

References:

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