Vol. 11 No. 12 (2019): On the distribution of primitive roots that are $(k,r)$-integers

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

  Teerapat Srichan, Pinthira Tangsupphathawat

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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.

  References