 

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 


Abstract
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
i_{p}(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
pappa@mat.uniroma3.it

