Related papers: The Arithmetic of Carmichael Quotients

We investigate two arithmetic functions naturally occurring in the study of the Euler and Carmichael quotients. The functions are related to the frequency of vanishing of the Euler and Carmichael quotients. We obtain several results…

We study the question of whether for each n there is another integer m with lambda(m)=lambda(n), where lambda is Carmichael's function. We give a "near" proof of the fact that this is the case unconditionally, and a complete conditional…

In this paper, the definitions of algebras of quotients and Martandale-like qoutients of Leibniz algebras are introduced and the interactions between the two quotients are determined. Firstly, some important properties which not only hold…

Ordinary differential equations have an arithmetic analogue in which functions are replaced by numbers and the derivation operator is replaced by a Fermat quotient operator. In this survey we explain the main motivations, constructions,…

Let $m$ be a Carmichael number and let $L$ be the least common multiple of $p-1$, where $p$ runs over the prime factors of $m$. We determine all the Carmichael numbers $m$ with a Fermat prime factor such that $L=2^{\alpha}P^2$, where $k\in…

We prove that every arithmetic progression either contains infinitely many Carmichael numbers or none at all. Furthermore, there is a simple criterion for determining which category a given arithmetic progression falls into. In particular,…

The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…

We describe an inequality of finite or infinite sequences of real numbers and their quotients. More precisely, we compare the quotient of H\"older functionals of two sequences of numbers with the sum of their quotients. In the last section…

We define a Carmichael number of order m to be a composite integer n such that nth-power raising defines an endomorphism of every Z/nZ-algebra that can be generated as a Z/nZ-module by m elements. We give a simple criterion to determine…

Consider exponential Carmichael function $\lambda^{(e)}$ such that $\lambda^{(e)}$ is multiplicative and $\lambda^{(e)}(p^a) = \lambda(a)$, where $\lambda$ is usual Carmichael function. We discuss the value of $\sum \lambda^{(e)}(n)$, where…

Intertwining analysis, algebra, numerical analysis and optimization, computing conjugate co-gradients of real-valued quotients gives rise to eigenvalue problems. In the linear Hermitian case, by inspecting optimal quotients in terms of…

We construct certain entire function $\lambda(s)$ which for integer s coincides with the well-known Keiper-Li coefficients, i.e. $\lambda(n)={\lambda}_{n}$. This is an even function ${\lambda}(s)={\lambda}(-s)$ and has an infinitude of…

We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…

By involving some exponential sums related to $\Lambda(n)$ in arithmetic progression, we can obtain some new results for von Mangoldt function over {\bf nonhomogeneous} Beatty sequences in arithmetic progressions, which improve some recent…

In this paper, we study the properties of Carmichael numbers, false positives to several primality tests. We provide a classification for Carmichael numbers with a proportion of Fermat witnesses of less than 50%, based on if the smallest…

Bounds and other relations involving variables connected with Carmichael numbers are reviewed and extended. Families of numbers or individual numbers attaining or approaching these bounds are given. A new algorithm for finding three-prime…

In this paper, we introduce the notion of system of quotients of Lie triple systems and investigate some properties which can be lifted from a Lie triple system to its systems of quotients. We relate the notion of Lie triple system of…

In this article we see that the value takes the Smarandache Function when it is applied to a perfect number.

Arithmetic differential equations are analogues of algebraic differential equations in which derivative operators acting on functions are replaced by Fermat quotient operators acting on numbers. Now, various remarkable transcendental…

Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…