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On the generalization of Mersenne and Gaussian Mersenne polynomials
The aim of this paper is to define the generalization of the Mersenne and Gaussian Mersenne polynomials with arbitrary initial values and study their...
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Computers As a Novel Mathematical Reality: III. Mersenne Numbers and Sums of Divisors
AbstractNowhere in mathematics is the progress resulting from the advent of computers as apparent as in the additive number theory. In this part, we...
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Mersenne und Torricelli
Marin Mersenne - bekannt durch die nach ihm benannten Primzahlen - hat sich in der Mathematik und der Mechanik weniger als Forscher, denn als...
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Mersenne Numbers in the Bases of Systems of Residual Classes when Transmitting Data in Serial Communication Channels
In this paper, we consider the system of residual classes for data representation in communication channels. In this case, it is possible to perform...
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Fermat
Obwohl Fermat auch auf anderen Gebieten der Mathematik Herausragendes geleistet hat, ist sein Name doch untrennbar mit der Zahlentheorie verbunden....
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Covering sumsets of a prime field and class numbers
We study covering sumsets of a prime field based on its multiplicative structure. By develo** various sufficient analytic and algebraic criteria...
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Applications
The purpose of this chapter is to review several diverse applications of the Lucas functions, particularly in the area of computational number...
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Die Abhandlung über die Spiralen (De infinitis spiralibus)
Torricelli hatte durch Mersenne erfahren, dass Roberval gefunden hat, dass die Länge eines Bogens der archimedischen Spirale gleich der Länge eines...
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Random Sequences in Vehicle Routing Problem
In this paper, we study the Capacitated Vehicle Routing Problem (CVRP) and implemented a simulation-based algorithm with different random number...
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The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows
The explicit determinants, inverses and eigenpairs of periodic tridiagonal Toeplitz-like matrices with perturbed rows are presented in this paper. We...
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Special Types of Primes
TheNumberMersenne|( French PrimeMersenne mathematician Marin Mersenne (1588–1648, see Fig. 4.1) studied numbers of the form...
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The Paradoxes of ZENO
The concept of infinity has been considered a difficult and problematic concept from antiquity to modern times. The view that DESCARTES occasionally...
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Unreliability of Available Pseudorandom Number Generators
AbstractThe problem of generating sequences of uniformly distributed pseudorandom numbers is considered. A simple visual test for estimating the...
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p-almost Hadamard matrices and \(\lambda \)-planes
In this work, we consider the p -almost Hadamard matrices and discuss about its connection with the orthogonal matrices corresponding to the finite...
