Results 21 to 30 of about 134 (102)
Some remarks on Euler's totient function [PDF]
, 2012 This article is a revision and extension of my previous article 'On the image of Euler's totient function' arXiv:0910 ...
Rodney Coleman
openalex +3 more sources
Linear equations with the Euler totient function [PDF]
Acta Arithmetica, 2007 Abstract : In this paper, we investigate linear relations among the Euler function of nearby integers. In particular, we study those positive integers n such that theta(n) = theta(n -1) + (n - 2), where theta is the Euler function. We prove that they form a set of asymptotic density zero. We also show that the sum of the reciprocals of the prime values
Luca, Florian, Stănică, Pantelimon
openaire +2 more sources
The Euler totient function on Lucas sequences
International Journal of Number Theory, 2022 In 2009, Luca and Nicolae [[Formula: see text], Integers 9 (2009) A30] proved that the only Fibonacci numbers whose Euler totient function is another Fibonacci number are [Formula: see text], and [Formula: see text]. In 2015, Faye and Luca [Pell numbers whose Euler function is a Pell number, Publ. Inst. Math.
openaire +3 more sources
Integer factoring and compositeness witnesses
Journal of Mathematical Cryptology, 2020 We describe a reduction of the problem of factorization of integers n ≤ x in polynomial-time (log x)M+O(1) to computing Euler’s totient function, with exceptions of at most xO(1/M) composite integers that cannot be factored at all, and at most x exp −cM ...
Pomykała Jacek, Radziejewski Maciej
doaj +1 more source
On sums involving divisor function, Euler's totient function, and floor function [PDF]
, 2023 Junya Sebata
+6 more sources
On the special cases of Carmichael's totient conjecture [PDF]
Notes on Number Theory and Discrete MathematicsEuler's totient function, φ(n), is the arithmetic function defined as the number of positive integers less than or equal to n that are relatively prime to n. In his 1922 paper [3], Professor R. D.
Anthony G. Shannon +3 more
doaj +1 more source
Some characterizations of totients
International Journal of Mathematics and Mathematical Sciences, 1996 An arithmetical function is said to be a totient if it is the Dirichlet convolution between a completely multiplicative function and the inverse of a completely multiplicative function. Euler's phi-function is a famous example of a totient.
Pentti Haukkanen
doaj +1 more source
A symmetric and a transposition cipher using the Euler’s totient function
Ceylon Journal of Science, 2019 Cryptography provides a method of exchanging sensitive information in a secured form while assuring its confidentiality. Encryption and decryption are the two steps in which the process gets completed.
A. P. Madushani, P. G. R. S. Ranasinghe
doaj +1 more source
A Generalisation of Euler Totient Function
, 2022 Euler's totient function, $φ(n)$, which counts how many of $0,1,\dots,n-1$ are coprime to $n$, has an explicit asymptotic lower bound of $n/\log \log n$, modulo some constant. In this note, we generalise $φ$; given an irreducible integer polynomial $P$, we define the arithmetic function $φ_P(n)$ that counts the amount of numbers among $P(0),P(1),\dots ...
openaire +3 more sources
On a sum involving the Euler totient function [PDF]
Indagationes Mathematicae, 2019 Let \(\alpha=4/\pi^2\) and \(\beta=1/3+\alpha\). In the paper under review, the author proves that as \(x\to\infty\), \[ \alpha\,x\log x+O(x)\leq\sum_{n\leq x}\varphi\left(\left\lfloor\frac{x}{n}\right\rfloor\right)\leq\beta\,x\log x+O(x), \] where \(\varphi\) is the Euler totient function.
openaire +3 more sources