Distance between consecutive elements of the multiplicative group of integers modulo n

Authors: Steven Brown

Source: Notes on Number Theory and Discrete Mathematics, Vol 30, Iss 1, Pp 081-099 (2024)

Subject Terms: sieves, sieve of eratosthenes, modular arithmetic, multiplicative group of integers modulo, chinese remainder theorem, inclusion-exclusion principle, euler's phi function, nagell's totient function, prime numbers, jacobsthal function, primorial, Mathematics, QA1-939

File Description: electronic resource

Relation: https://nntdm.net/papers/nntdm-30/NNTDM-30-1-081-099.pdf; https://doaj.org/toc/1310-5132; https://doaj.org/toc/2367-8275

Access URL: https://doaj.org/article/18a74519b5fe4804aa081ffacc0ddf9c

A class of solutions of the equation d(n²) = d(φ(n))

Authors: Zahra Amroune, Djamel Bellaouar, Abdelmadjid Boudaoud

Source: Notes on Number Theory and Discrete Mathematics, Vol 29, Iss 2, Pp 284-309 (2023)

Subject Terms: diophantine equations, euler's phi function, Mathematics, QA1-939

File Description: electronic resource

Relation: https://nntdm.net/papers/nntdm-29/NNTDM-29-2-284-309.pdf; https://doaj.org/toc/1310-5132; https://doaj.org/toc/2367-8275

Access URL: https://doaj.org/article/41122e8f81a64ac583b8bfa4a0557f2e

On Determination of

Authors: Debnath, Anjan^Aff11, Adhikari, Avishek^Aff12

Contributors: Cavas-Martínez, Francisco, Series Editor^Aff1, Chaari, Fakher, Series Editor^Aff2, Gherardini, Francesco, Series Editor^Aff3, Haddar, Mohamed, Series Editor^Aff4, Ivanov, Vitalii, Series Editor^Aff5, Kwon, Young W., Series Editor^Aff6, Trojanowska, Justyna, Series Editor^Aff7, Mishra, S. R., editor^Aff8, Dhamala, T. N., editor^Aff9, Makinde, O. D., editor^Aff10

Source: Recent Trends in Applied Mathematics : Select Proceedings of AMSE 2019. :47-58

A simple proof of generalizations of number-theoretic sums

Authors: Yanapat Tongron, Narakorn Rompurk Kanasri

Source: Songklanakarin Journal of Science and Technology (SJST), Vol 44, Iss 2, Pp 450-458 (2022)

Subject Terms: arithmetic function, euler’s phi-function, möbius function, möbius inversion formula, Technology, Technology (General), T1-995, Science, Science (General), Q1-390

File Description: electronic resource

Relation: https://rdo.psu.ac.th/sjst/journal/44-2/22.pdf; https://doaj.org/toc/0125-3395

Access URL: https://doaj.org/article/8863d723529544afa4ba7555e3ea076a

Inequalities for the Arithmetical Functions of Euler and Dedekind

Authors: Alzer, Horst^{Aff1, IDCMJ2020053018_cor1}, Kwong, Man Kam

Source: Czechoslovak Mathematical Journal. 70(3):781-791

A Note on Variants of Euler's Φ-Function

Authors: Sertbas, Doga Can, Goral, Haydar, Buyukasik, Engin

Subject Terms: Bernoulli numbers, Euler's phi-function, prime number theory

Relation: Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı; https://hdl.handle.net/11147/14645; https://doi.org/10.5486/PMD.2024.9674; 105; WOS:001303046100005; Q3

Availability: https://hdl.handle.net/11147/14645
https://doi.org/10.5486/PMD.2024.9674

New properties of even perfect numbers and the mathematical reasons that suggest there are no odd perfect numbers ; Nuevas propiedades de números perfectos pares y las razones matemáticas que sugieren que no existen números perfectos impares

Authors: Villarroel, Alexander, Villarroel, Francisco

Source: Impacto Científico; Vol. 18 Núm. 1 (2023): Revista Impacto Científico; 129-162 ; 2542-3207 ; 1856-5042

Subject Terms: Euler's phi function, even perfect numbers, odd perfect numbers, triangular numbers, hexagonal numbers, Función phi de Euler, números perfectos pares, números perfectos impares, números triangulares, números hexagonales

File Description: application/pdf

Relation: https://www.produccioncientificaluz.org/index.php/impacto/article/view/40290/45723; https://www.produccioncientificaluz.org/index.php/impacto/article/view/40290

Availability: https://www.produccioncientificaluz.org/index.php/impacto/article/view/40290

Representation Numbers of Stars

Authors: Akhtar, Reza^{aff1_w2aab2b8c15b1b7b1aab1b3b3Aa}, Evans, Anthony B.^{aff2_w2aab2b8c15b1b7b1aab1b3b4Aa}, Pritikin, Dan^{aff1_w2aab2b8c15b1b7b1aab1b3b3Aa}

Source: Integers. 10(6):733-745

Availability: https://www.degruyter.com/document/doi/10.1515/integ.2010.054/html

An extension of a result of Lehmer on numbers coprime to n

Authors: CODECA', Paolo, NAIR, Mohan K.

Source: The Ramanujan Journal. 16:59-71

Subject Terms: 0101 mathematics, 01 natural sciences, Euler's phi-function, Discrepancy, Lehmer's bounds

Access URL: https://link.springer.com/article/10.1007/s11139-007-9095-8
https://core.ac.uk/display/9358760

Some Mean Values Related to Average Multiplicative Orders of Elements in Finite Fields: Some mean values related to average multiplicative orders of elements in finite fields

Authors: Florian Luca

Source: The Ramanujan Journal. 9:33-44

Subject Terms: Euler's phi function, enumeration problems, Asymptotic results on counting functions for algebraic and topological structures, cyclic groups, finite fields, asymptotic estimates, 0101 mathematics, average order, Asymptotic enumeration, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s11139-005-0823-7

Criptografia: A Teoria e a prática em sala de aula ; Cryptography: Theory and practice in the classroom

Authors: Reis, Matheus Alves Machado

Contributors: Coelho, Francielle Rodrigues de Castro, http://buscatextual.cnpq.br/buscatextual/visualizacv.do, jsessionid=E6094A90D6CE33CC8D4846B98CDA5944.buscatextual_0, Silva, Flávia Souza Machado da, http://lattes.cnpq.br/9625562877284120, Galves, Ana Paula Tremura, http://lattes.cnpq.br/2733373203786930

Subject Terms: Congruência modular, Função phi de Euler, Cifra de César, Criptografia RSA, Modular congruence, Euler’s phi function, Caesar’s cipher, RSA cryptography, CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA::TEORIA DOS NUMEROS, Matemática, Criptografia de dados (Computação), Proteção de dados

File Description: application/pdf

Relation: https://repositorio.ufu.br/handle/123456789/39270; http://doi.org/10.14393/ufu.di.2023.517

Availability: https://repositorio.ufu.br/handle/123456789/39270
https://doi.org/10.14393/ufu.di.2023.517

On the determinants of divisor matrices

Authors: R. H. Jeurissen

Source: Discrete Mathematics. 265:375-383

Subject Terms: Euler's phi function, divisor matrices, Arithmetic progressions, Discrete Mathematics and Combinatorics, determinants, Determinants, permanents, traces, other special matrix functions, 0102 computer and information sciences, 0101 mathematics, Kronecker products of matrices, 01 natural sciences, Divisor matrices, Determinants, Theoretical Computer Science

File Description: application/xml

Access URL: https://zbmath.org/1915555
https://doi.org/10.1016/s0012-365x(02)00880-4
https://www.sciencedirect.com/science/article/pii/S0012365X02008804
https://dblp.uni-trier.de/db/journals/dm/dm265.html#Jeurissen03
http://www.sciencedirect.com/science/article/pii/S0012365X02008804

On some problems of Mąkowski–Schinzel and Erdős concerning the arithmetical functions φ and σ: On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions \(\varphi\) and \(\sigma\)

Authors: Florian Luca, Carl Pomerance

Source: Colloquium Mathematicum. 92:111-130

Subject Terms: sum-of-divisors function, maximal order, normal order, Arithmetic functions, related numbers, inversion formulas, Asymptotic results on arithmetic functions, Rate of growth of arithmetic functions, 0101 mathematics, average order, Euler's phi-function, 01 natural sciences

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/87975?download.pdf
https://www.impan.pl/shop/publication/transaction/download/product/87975?download.pdf
https://eudml.org/doc/283450
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/92/1/87975/on-some-problems-of-m-akowski-8211-schinzel-and-erdos-concerning-the-arithmetical-functions-phi-and-sigma
http://journals.impan.pl/cgi-bin/doi?cm92-1-10
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-10

On the distribution of the density of maximal order elements in general linear groups

Authors: Aivazidis, S., Sofos, E.

Source: The Ramanujan Journal: An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan. October 2015 38(1):35-59

Some characterizations of totients

Authors: Haukkanen, Pentti

Contributors: University of Tampere

Source: International Journal of Mathematics and Mathematical Sciences, Vol 19, Iss 2, Pp 209-217 (1996)

Subject Terms: arithmetical identities, completely multiplicative functions, Matematiikka - Mathematics, Arithmetic functions, related numbers, inversion formulas, 0102 computer and information sciences, multiplicative arithmetical functions, Euler's phi-function, 01 natural sciences, totient, totient functions, arithmetical function, QA1-939, 0101 mathematics, Mathematics, Dirichlet convolution

File Description: application/xml; fulltext

Access URL: http://downloads.hindawi.com/journals/ijmms/1996/129618.pdf
https://doaj.org/article/fc793f01b6494c4981836224a1bff81e
https://trepo.tuni.fi/handle/10024/99109
https://downloads.hindawi.com/journals/ijmms/1996/129618.pdf
https://www.hindawi.com/journals/ijmms/1996/129618/
https://trepo.tuni.fi/handle/10024/99109

On Nontotients: On nontotients

Authors: Zhang, M.Z.

Source: Journal of Number Theory. 43:168-172

Subject Terms: 03 medical and health sciences, Algebra and Number Theory, 0302 clinical medicine, 05 social sciences, Arithmetic functions, related numbers, inversion formulas, Euler's phi-function, 0503 education, nontotient

File Description: application/xml

Periodicity on discrete dynamical systems generated by a class

Authors: Ignacio Bajo, Eduardo Liz, E. T. S. E. Telecomunicación, Campus Marcosende

Contributors: The Pennsylvania State University CiteSeerX Archives

Source: http://www.dma.uvigo.es/~eliz/pdf/jdea3.pdf.

Subject Terms: Global periodicity, Discrete dynamical system, Periodic point, Rational map, Euler’s phi- function

File Description: application/pdf

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.537.2713; http://www.dma.uvigo.es/~eliz/pdf/jdea3.pdf

Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.537.2713
http://www.dma.uvigo.es/~eliz/pdf/jdea3.pdf

Average Order in Cyclic Groups

Authors: Joachim Von Zur Gathen, Arnold Knopfmacher, Florian Luca, Lutz G. Lucht, Igor E. Shparlinski

Contributors: The Pennsylvania State University CiteSeerX Archives

Source: http://www.wits.ac.za/science/number_theory/./research/gathen.ps.

Subject Terms: Average order, enumeration problems, cyclic groups, finite fields, asymptotic estimates, Euler's phi function, Euler products, Dirichlet convolution

File Description: application/postscript

Relation: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.5638; http://www.wits.ac.za/science/number_theory/./research/gathen.ps

Availability: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.5638
http://www.wits.ac.za/science/number_theory/./research/gathen.ps

Development of an Arithmetic Function using Euler’s Phi Function and Study of its Properties

Authors: Maharjan, Nischal, Budha, Bhupendra

Source: Journal of the Institute of Engineering; Vol. 15 No. 2 (2019); 147-151 ; 1810-3383

Subject Terms: arithmetic function, Euler’s phi function, prime numbers

Subject Geographic: Engineering

File Description: application/pdf

Relation: https://nepjol.info/index.php/JIE/article/view/27660/22852; https://nepjol.info/index.php/JIE/article/view/27660

Availability: https://nepjol.info/index.php/JIE/article/view/27660

On the Proof of a Theorem of Pálfy

Authors: Dobson, Edward

Source: The Electronic Journal of Combinatorics. 13

Subject Terms: CI-group, Euler's phi function, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

File Description: text/url

Access URL: https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1n16/pdf
https://www.emis.de/journals/EJC/ojs/index.php/eljc/article/view/v13i1n16
https://dblp.uni-trier.de/db/journals/combinatorics/combinatorics13.html#Dobson06
https://www.combinatorics.org/Volume_13/Abstracts/v13i1n16.html
https://repozitorij.upr.si/IzpisGradiva.php?id=1454
https://hdl.handle.net/20.500.12556/RUP-1454