Armenian Journal of Mathematics http://armjmath.sci.am/index.php/ajm 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 nerses@instmath.sci.am (Anry Nersessian) ajm@instmath.sci.am (Linda Khachatryan) Thu, 26 Dec 2019 13:24:47 +0000 OJS 3.1.2.4 http://blogs.law.harvard.edu/tech/rss 60 On the distribution of primitive roots that are $(k,r)$-integers http://armjmath.sci.am/index.php/ajm/article/view/298 <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 http://creativecommons.org/licenses/by/4.0 http://armjmath.sci.am/index.php/ajm/article/view/298 Fri, 13 Dec 2019 17:51:00 +0000