Armenian Journal of Mathematics, 11(12)
2022; 1–12
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On the distribution of primitive roots that are ( k , r ) -integers

Teerapat Srichan*, Pinthira Tangsupphathawat

Received: 2024-12-11 · Published: 2022-09-15

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CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
On the distribution of primitive roots that are ( k , r ) -integers
Authors
Teerapat Srichan, Pinthira Tangsupphathawat
Source journal
Armenian Journal of Mathematics, 11(12)
Published
2022-09-15
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2019.11.12-1-12

Abstract

Let kk and rr be fixed integers with 1<r<k1<r<k. A positive integer is called rr-free if it is not divisible by the rthrth power of any prime. A positive integer nn is called a (k,r)(k,r)-integer if nn is written in the form akbakb where bb is an rr-free integer. Let pp be an odd prime and let x>1x>1 be a real number. In this paper an asymptotic formula for the number of (k,r)(k,r)-integers which are primitive roots modulo pp and do not exceed xx is obtained.
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