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The article studies the cubic mapping graph $Γ (n)$ of $ℤ_{n} [i]$ , the ring of Gaussian integers modulo $n$ . For each positive integer $n > 1$ , the number of fixed points and the in-degree of the elements $\bar{1}$ and $\bar{0}$ in $Γ (n)$ are found. Moreover, complete characterizations in terms of $n$ are given in which $Γ_{2} (n)$ is semiregular, where $Γ_{2} (n)$ is induced by all the zero-divisors of $ℤ_{n} [i]$ .

The cyclotomic numbers of order twenty

Joseph Muskat, A. Whiteman (1970)

Acta Arithmetica

The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives

Gopalakrishna Hejmadi Gadiyar, Ramanathan Padma (2018)

Czechoslovak Mathematical Journal

We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.

The enumeration of simple permutations.

Albert, M.H., Atkinson, M.D., Klazar, M. (2003)

Journal of Integer Sequences [electronic only]

The existence of solutions of the generalized pseudoprime congruence $a^{f (n)} \equiv b^{f (n)} (m o d n)$

Wayne L. McDaniel (1990)

Colloquium Mathematicae

The fundamental constituents of iteration digraphs of finite commutative rings

Jizhu Nan, Yangjiang Wei, Gaohua Tang (2014)

Czechoslovak Mathematical Journal

For a finite commutative ring $R$ and a positive integer $k ⩾ 2$ , we construct an iteration digraph $G (R, k)$ whose vertex set is $R$ and for which there is a directed edge from $a \in R$ to $b \in R$ if $b = a^{k}$ . Let $R = R_{1} \oplus ... \oplus R_{s}$ , where $s > 1$ and $R_{i}$ is a finite commutative local ring for $i \in {1, ..., s}$ . Let $N$ be a subset of ${R_{1}, \dots, R_{s}}$ (it is possible that $N$ is the empty set $\emptyset$ ). We define the fundamental constituents $G_{N}^{*} (R, k)$ of $G (R, k)$ induced by the vertices which are of the form ${(a_{1}, \dots, a_{s}) \in R : a_{i} \in D (R_{i})$ if $R_{i} \in N$ , otherwise $a_{i} \in U (R_{i}), i = 1, ..., s},$ where U $(R)$ denotes the unit group of $R$ and D $(R)$ denotes the zero-divisor set of $R$ . We investigate...

The Gergonne $m$ -pile trick and the base $m$ counting system. (El truco de $m$ pilas de Gergonne y el sistema de numeración de base $m$ .)

Quintero, Roy (2006)

Boletín de la Asociación Matemática Venezolana

The Kazandzidis supercongruences. A simple proof and an application

Alain Robert, Maxime Zuber (1995)

Rendiconti del Seminario Matematico della Università di Padova

The Lucas congruence for Stirling numbers of the second kind

Roberto Sánchez-Peregrino (2000)

Acta Arithmetica

0. Introduction. The numbers introduced by Stirling in 1730 in his Methodus differentialis [11], subsequently called “Stirling numbers” of the first and second kind, are of the greatest utility in the calculus of finite differences, in number theory, in the summation of series, in the theory of algorithms, in the calculation of the Bernstein polynomials [9]. In this study, we demonstrate some properties of Stirling numbers of the second kind similar to those satisfied by binomial coefficients; in...

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Displaying 321 – 340 of 378

Sur le nombre des racines et des facteurs irréductibles d'une congruence donnée

Sur les congruences identiques

Sur les nombres de la forme $X^{2} + X Y + Y^{2}$

Sur les racines primitives

Sur les racines primitives

Sur quelques théorèmes d'arithmétique

The cube of the Fermat quotient.

The cubic mapping graph for the ring of Gaussian integers modulo $n$

The cyclotomic numbers of order twenty

The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives

The enumeration of simple permutations.

The existence of solutions of the generalized pseudoprime congruence $a^{f (n)} \equiv b^{f (n)} (m o d n)$

The fundamental constituents of iteration digraphs of finite commutative rings

The Gergonne $m$ -pile trick and the base $m$ counting system. (El truco de $m$ pilas de Gergonne y el sistema de numeración de base $m$ .)

The Kazandzidis supercongruences. A simple proof and an application

The Lucas congruence for Stirling numbers of the second kind

The number of restricted solutions of some systems of linear congruences

The number of solutions of a special quadratic congruence

The primary pretenders

The role of semigroups in the elementary theory of numbers

Currently displaying 321 – 340 of 378