http://armjmath.sci.am/index.php/ajm/issue/feedArmenian Journal of Mathematics2019-12-26T13:24:47+00:00Anry Nersessiannerses@instmath.sci.amOpen Journal SystemsArmenian Journal of Mathematics Armen.J.Math., original research papers, survey articles, areas of mathematics, theoretical mathematics, applications, review articles, short communications, conference proceedings, algorithms, Ph.D and doctoral thesisâ€™s.http://armjmath.sci.am/index.php/ajm/article/view/298On the distribution of primitive roots that are $(k,r)$-integers2019-12-26T13:24:41+00:00Teerapat Srichanfscitrp@ku.ac.thPinthira Tangsupphathawatt.pinthira@hotmail.com<p style="text-align: justify;">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.</p> <p style="text-align: justify;">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.</p>2019-12-13T17:51:00+00:00Copyright (c) 2019 Armenian Journal of Mathematics