Armenian Journal of Mathematics 2019-12-26T13:24:47+00:00 Anry Nersessian Open Journal Systems 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. On the distribution of primitive roots that are $(k,r)$-integers 2019-12-26T13:24:41+00:00 Teerapat Srichan Pinthira Tangsupphathawat <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> 2019-12-13T17:51:00+00:00 Copyright (c) 2019 Armenian Journal of Mathematics