On the distribution of primitive roots that are $(k,r)$-integers

Armenian Journal of Mathematics

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Title On the distribution of primitive roots that are $(k,r)$-integers
Creator Srichan, Teerapat
Tangsupphathawat, Pinthira
Subject $(k,r) $-integer
primitive root
Description Let $k$ and $r$ be fixed integers with $1<r<k$. 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 $x>1$ be a real number.
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.
Publisher National Academy of Sciences of Armenia
Date 2019-12-13
Type info:eu-repo/semantics/article
Peer-reviewed Article
Format application/pdf
Identifier http://armjmath.sci.am/index.php/ajm/article/view/298
Source Armenian Journal of Mathematics; Vol. 11 No. 12 (2019): On the distribution of primitive roots that are $(k,r)$-integers ; 1-12
Language eng
Relation http://armjmath.sci.am/index.php/ajm/article/view/298/153
Rights Copyright (c) 2019 Armenian Journal of Mathematics

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