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

## 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.

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## Published

2019-12-13

## How to Cite

*Armenian Journal of Mathematics*,

*11*(12), 1–12. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/298

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## Section

Articles