Affiliation:
1. Department of Mathematics, University of California Los Angeles, 520 Portola Plaza Math Science Building 6617A, Los Angeles, CA 90095, USA
Abstract
Let [Formula: see text] be an integer. Denote by [Formula: see text] the multiplicative order of [Formula: see text] modulo integer [Formula: see text]. We prove that there is a positive constant [Formula: see text] such that if [Formula: see text], then [Formula: see text] where [Formula: see text] It was known for [Formula: see text] in [P. Kurlberg and C. Pomerance, On a problem of Arnold: The average multiplicative order of a given integer, Algebra Number Theory 7 (2013) 981–999] in which they refer to [F. Luca and I. E. Shparlinski, Average multiplicative orders of elements modulo [Formula: see text], Acta Arith. 109(4) (2003) 387–411.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
1 articles.
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