On the distribution of primitive roots that are $(k,r)$-integers

Authors

  • Teerapat Srichan Kasetsart University
  • Pinthira Tangsupphathawat Phranakorn Rajabhat University

DOI:

https://doi.org/10.52737/18291163-2019.11.12-1-12

Keywords:

$(k,r) $-integer, primitive root

Abstract

Let $k$ and $r$ be fixed integers with $1<r<k$. A positive integer is called $r$-free if it is not divisible by the $r^{th}$ power of any prime. A positive integer $n$ is called a $(k,r)$-integer if $n$ is written in the form $a^kb$ where $b$ is an $r$-free integer. Let $p$ be an odd prime and let $x>1$ be a real number.

In this paper an asymptotic formula for the number of $(k,r)$-integers which are primitive roots modulo $p$ and do not exceed $x$ is obtained.

Downloads

Published

2019-12-13 — Updated on 2022-09-15

Versions

How to Cite

On the distribution of primitive roots that are $(k,r)$-integers. (2022). Armenian Journal of Mathematics, 11(12), 1-12. https://doi.org/10.52737/18291163-2019.11.12-1-12 (Original work published 2019)