Results 11 to 20 of about 134 (102)
On a group-theoretical generalization of the Euler's totient function [PDF]
Indian Journal of Pure and Applied Mathematics, 2021 Let $G$ be a finite group and $φ(G)=|\{a\in G \mid o(a)=\exp(G)\}|$, where $o(a)$ denotes the order of $a$ in $G$ and $\exp(G)$ denotes the exponent of $G$. Under a natural hypothesis, in this note we determine the groups $G$ such that $\forall\, H,K\leq G$, $H\subseteq K$ implies $φ(H)\midφ(K)$. This partially answers Problem 5.4 in \cite{6}.
Marius Tărnăuceanu
openalex +4 more sources
The investigation of Euler's totient function preimages [PDF]
Journal of Applied Mathematics and Computation, 2018 "Sixth International Conference on Analytic Number Theory and 11 Spatial Tessellations. Voronoy Conference"
Ruslan Skuratovskii
openalex +4 more sources
On the image of Euler's totient function [PDF]
, 2009 In this article we study certain properties of the image of Euler's totient function; we also consider the structure of the preimage of certain elements of the image of this function.
Rodney Coleman
openalex +3 more sources
Sums related to Euler's totient function [PDF]
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/φ(a_{n}))^{s}$, where $φ$ is Euler's totient function, $s\in \mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ φ(a_{n})>
Artyom Olegovich Radomskii
openalex +3 more sources
On a Lehmer problem concerning Euler's totient function [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 2003 \textit{D. H. Lehmer} [Bull. Am. Math. Soc. 38, 745--751 (1932; Zbl 0005.34302)] asked whether there exists any composite number \(n\) such that \(\varphi (n)| n-1\), that is, (*) \(M \varphi (n)=n-1\) for some \(M\). This question is still open. The present authors review some facts concerning (*) presented in the literature and show that if \(n ...
Aleksander Grytczuk, Marek Wójtowicz
openalex +3 more sources
Jacobsthal's function and a generalisation of Euler's totient [PDF]
, 2012 Jacobsthal's function h(k) represents the smallest number m such that every sequence of m consecutive integers contains an integer coprime to P_k, the product of the first k primes. The best known bound on h(k) is h(k) < C (k ln k)^2 for some unknown constant C, due to Iwaniec.
Fintan Costello, Paul Watts
openalex +3 more sources
PARTITION FUNCTION IN TERMS OF THE EULER'S TOTIENT FUNCTION
Merca obtained an expression involving the partition function and Euler’s totient function , which can be written using a lower triangular matrix whose inversión gives the relation deduced by Alegri-Prajapati-(López-Bonilla) for in terms ...
L. I. Mar-Escoto** & J. Lopez-Bonilla** R. Sivaraman*
+5 more sources
Density properties of fractions with Euler's totient function [PDF]
Involve, a Journal of MathematicsWe prove that for all constants $a\in\N$, $b\in\Z$, $c,d\in\R$, $c\neq 0$, the fractions $ϕ(an+b)/(cn+d)$ lie dense in the interval $]0,D]$ (respectively $[D,0[$ if $c<0$), where $D=aϕ(\gcd(a,b))/(c\gcd(a,b))$. This interval is the largest possible, since it may happen that isolated fractions lie outside of the interval: we prove a complete ...
Karin Halupczok, Marvin Ohst
openalex +3 more sources
The Euler’s totient function in canonical hypergroups
Indian Journal of Pure and Applied Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sonea, Andromeda Cristina, Davvaz, Bijan
openaire +1 more source
The Order of Euler’s Totient Function
, 2021 The Mobius function is commonly used to define Euler’s totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) is used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).
Darrell Cox +2 more
openaire +2 more sources