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

Let kk and rr be fixed integers with 1<r<k1<r<k. A positive integer is called rr-free if it is not divisible by the rthrth power of any prime. A positive integer nn is called a (k,r)(k,r)-integer if nn is written in the form akbakb where bb is an rr-free integer. Let pp be an odd prime and let x>1x>1 be a real number.

In this paper an asymptotic formula for the number of (k,r)(k,r)-integers which are primitive roots modulo pp and do not exceed xx is obtained.

DOI: 10.52737/18291163-2019.11.12-1-12 Armenian Journal of Mathematics, 11(12) 1-12

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Keywords

( k , r ) -integer, primitive root

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