Vol. 9, No. 2, 2020

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Square-full primitive roots in arithmetic progressions

Vichian Laohakosol, Teerapat Srichan and Pinthira Tangsupphathawat

Vol. 9 (2020), No. 2, 187–202
DOI: 10.2140/moscow.2020.9.187
Abstract

An asymptotic estimate for the number of positive primitive roots which are square-full integers in arithmetic progressions is derived. The employed method combines two techniques and is based on the character-sum method involving two characters; one character is to take care of being a primitive root, based on a result of Shapiro, and the other character is to take care of being square-full, based on a result of Munsch.

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Keywords
arithmetic progressions, primitive roots, square-full numbers
Mathematical Subject Classification
Primary: 11A07, 11B25, 11N37, 11N69
Milestones
Received: 26 May 2020
Accepted: 23 June 2020
Published: 7 August 2020
Authors
Vichian Laohakosol
Department of Mathematics, Faculty of Science
Kasetsart University
Bangkok
Thailand
Teerapat Srichan
Department of Mathematics, Faculty of Science
Kasetsart University
Bangkok
Thailand
Pinthira Tangsupphathawat
Department of Mathematics, Faculty of Science and Technology
Phranakorn Rajabhat University
Bangkok
Thailand