New York Journal of Mathematics
Volume 9 (2003) 331-344


Francesco Pappalardi

Square free values of the order function

Published: December 7, 2003
Keywords: Square free integers, Carmichael function, Wirsing theorem, Chebotarev density theorem
Subject: 11N37, 11N56

Given a∈Z \ {±1,0}, we consider the problem of enumerating the integers m coprime to a such that the order of a modulo m is square free. This question is raised in analogy to a result recently proved jointly with F. Saidak and I. Shparlinski where square free values of the Carmichael function are studied. The technique is the one of Hooley that uses the Chebotarev Density Theorem to enumerate primes for which the index ip(a) of a modulo p is divisible by a given integer.

Author information

Dipartimento di Matematica, Università degli Studi Roma Tre, Largo S. L. Murialdo 1, Roma, 00146, Italy