Arithmetic properties of $φ(n)/λ(n)$ and the structure of the multiplicative group modulo $n$

William D. Banks, Florian Luca, Igor E. Shparlinski

Type: Article

Publication Date: 2006-03-31

Citations: 6

DOI: https://doi.org/10.4171/cmh/40

Abstract

For a positive integer n , we let \varphi(n) and \lambda(n) denote the Euler function and the Carmichael function, respectively. We define \xi(n) as the ratio \varphi(n)/\lambda(n) and study various arithmetic properties of \xi(n) .

Locations

Commentarii Mathematici Helvetici - View - PDF
MOspace Institutional Repository (University of Missouri) - View - PDF

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Works That Cite This (6)

Action	Title	Year	Authors
+ PDF Chat	Values of the Euler Function in Various Sequences	2005	William D. Banks Kevin Ford Florian Luca Francesco Pappalardi Igor E. Shparlinski
+ PDF Chat	Coincidences in the values of the Euler and Carmichael functions	2006	William D. Banks John Friedlander Florian Luca Francesco Pappalardi Igor E. Shparlinski
+	The Number of Non-cyclic Sylow Subgroups of the Multiplicative Group Modulo <i>n</i>	2020	Paul Pollack
+	Davenport constant for finite abelian groups	2008	Emre Alkan
+	On the average number of divisors of the Euler function	2007	Florian Luca Carl Pomerance
+ PDF Chat	Compositions with the euler and carmichael functions	2005	William D. Banks Florian Luca Filip Saidak P. StĂ nicĂ

Works Cited by This (17)

Action	Title	Year	Authors
+ PDF Chat	Carmichael's lambda function	1991	P. Erdős Carl Pomerance Eric Schmutz
+	Multiplicative Number Theory	1980	H. Davenport
+	On the distribution of amicable numbers. II.	1981	Carl Pomerance
+ PDF Chat	Multiplicative structure of values of the Euler function	2004	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski
+	On the Normal Behavior of the Iterates Of some Arithmetic Functions	1990	Paul Erdős Andew Granvilie Carl Pomerance Claudia Spiro
+	The Prime k-Tuplets Conjecture on Average	1990	Antal Balog
+ PDF Chat	Probabilistic Methods in the Theory of Numbers	1964	Jonas Kubilius
+ PDF Chat	On the number of restricted prime factors of an integer. I	1976	Karl K. Norton
+ PDF Chat	Shifted primes without large prime factors	1998	Roger C. Baker G. Harman
+	Das asymptotische Verhalten von Summen �ber multiplikative Funktionen	1961	Eduard Wirsing