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 thesisâ€™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 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 2019-12-13 2019-12-13 11 12 1 12