Armenian Journal of Mathematics Armenian 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 thesis’s. National Academy of Sciences of Armenia en-US Armenian Journal of Mathematics 1829-1163 On the distribution of primitive roots that are $(k,r)$-integers <p style="text-align: justify;">Let $k$ and $r$ be fixed integers with $1&lt;r&lt;k$. 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 $x&gt;1$ 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> Teerapat Srichan Pinthira Tangsupphathawat Copyright (c) 2019 Armenian Journal of Mathematics 2019-12-13 2019-12-13 11 12 1 12