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. en-US (Anry Nersessian) (Linda Khachatryan) Thu, 26 Dec 2019 13:24:47 +0000 OJS 60 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 Fri, 13 Dec 2019 17:51:00 +0000