Results 31 to 40 of about 134 (102)

A note on newly introduced arithmetic functions φ+ and σ+ [PDF]

Notes on Number Theory and Discrete Mathematics
In a recent paper [7], the authors introduced new arithmetic functions φ⁺, σ⁺ related to the classical functions φ, and σ, respectively. In this note, we study the behavior of Σ_{n≤x, ω(n)=2}(φ⁺-φ)(n), and Σ_{n≤x, ω(n)=2}(σ⁺-σ)(n), for any real number x ...
Sagar Mandal
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Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, I [PDF]

Notes on Number Theory and Discrete Mathematics
The aim of this work is to present a method using the cyclic sequences {Mₖ},{θₜₖ} and {ψₜₖ} in the finite fields 𝔽_ρ, with ρ a prime, that yield divisors of Mersenne, Fermat and Lehmer numbers.
A. M. S. Ramasamy
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Distance between consecutive elements of the multiplicative group of integers modulo n [PDF]

Notes on Number Theory and Discrete Mathematics
For a prime number p, we consider its primorial P:=p# and U(P):=(ℤ/Pℤ)^× the set of elements of the multiplicative group of integers modulo P which we represent as points anticlockwise on a circle of perimeter P.
Steven Brown
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Diophantine equations involving the Euler totient function [PDF]

Journal of Number Theory, 2020
We deal with various Diophantine equations involving the Euler totient function and various sequences of numbers, including factorials, powers, and Fibonacci sequences.
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On a generalization of the Euler totient function [PDF]

Monatshefte für Mathematik, 2012
A polynomial Euler product is a function \(F(s) = \prod_p \prod_{j=1}^d (1-\alpha_j(p)p^{-s})^{-1}\), which is absolutely convergent for \(s= \sigma + it\) with \(\sigma > 1\). Here \(p\) runs over the primes and the complex numbers \(\alpha_j(p)\) have norm at most \(1\) for all \(p\) and \(1 \leq j \leq d\).
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On The Smarandache Power Function And Euler Totient Function

, 2008
The main purpose of this paper is using the elementary method to study the solutions of an equation, and give its all positive integer solutions for k = 1; 2; 3.
Tian, Chengliang, Li, Xiaoyan
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Generalization of an Identity about Euler’s totient function

Irish Mathematical Society Bulletin, 2019
n ...
Bai, M., Chu, W., Li, N. N.
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Iterating the Sum of Möbius Divisor Function and Euler Totient Function [PDF]

Mathematics, 2019
In this paper, according to some numerical computational evidence, we investigate and prove certain identities and properties on the absolute Möbius divisor functions and Euler totient function when they are iterated. Subsequently, the relationship between the absolute Möbius divisor function with Fermat primes has been researched and some results have
Daeyeoul Kim, Umit Sarp, Sebahattin Ikikardes   +2 more
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Diophantine equations involving Euler’s totient function

Acta Arithmetica, 2019
In this paper, we consider the equations involving Euler's totient function $ϕ$ and Lucas type sequences. In particular, we prove that the equation $ϕ(x^m-y^m)=x^n-y^n$ has no solutions in positive integers $x, y, m, n$ except for the trivial solutions $(x, y, m , n)=(a+1, a, 1, 1)$, where $a$ is a positive integer, and the equation $ϕ((x^m-y^m)/(x-y))=
Chen, Yong-Gao, Tian, Hao
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Sparse subsets of the natural numbers and Euler’s totient function [PDF]

Proceedings - Mathematical Sciences, 2019
In this article, we investigate sparse subsets of the natural numbers and study the sparseness of some sets associated with the Euler's totient function $ϕ$ via the property of `Banach Density'. These sets related to the totient function are defined as follows: $V:=ϕ(\mathbb{N})$ and $N_i:=\{N_i(m)\colon m\in V \}$ for $i = 1, 2, 3,$ where $N_1(m)=\max\
Das, Mithun Kumar, Eyyunni, Pramod, Patil, Bhuwanesh Rao   +2 more
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