Armenian Journal of Mathematics

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

Srichan, Teerapat and Pinthira, Tangsupphathawat (2019) On the distribution of primitive roots that are $(k,r) $-integers. Armenian Journal of Mathematics, 11 (12). pp. 1-12. ISSN 1829-1163

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:$(k,r) $-integer, primitive root
Subjects:11-xx Number theory
ID Code:855
Deposited By:Professor Anry Nersesyan
Deposited On:26 Dec 2019 20:29
Last Modified:26 Dec 2019 20:30

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