On the distribution of primitive roots that are $(k,r)$-integers
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2019-12-01
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| Series: | Armenian Journal of Mathematics |
| Subjects: | |
| Online Access: | http://test.armjmath.sci.am/index.php/ajm/article/view/298 |
| Summary: | 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.
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| ISSN: | 1829-1163 |