Results 21 to 30 of about 12,326 (180)

Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II [PDF]

Notes on Number Theory and Discrete Mathematics
Let ρ be an odd prime ≥ 11. In Part I, starting from an M-cycle in a finite field 𝔽_ρ, we have established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
doaj   +1 more source

Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications [PDF]

, 2015
We are considering the class of heterotic $\mathcal{N}=(2,2)$ Landau-Ginzburg orbifolds with 9 fields corresponding to $A_1^9$ Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under mirror ...
Blaszczyk, Michael, Oehlmann, Paul-Konstantin   +1 more
core   +1 more source

Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix

Abstract and Applied Analysis, 2015
The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed.
Yanpeng Zheng, Sugoog Shon
doaj   +1 more source

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
doaj   +1 more source

Fast integer multiplication using generalized Fermat primes [PDF]

, 2018
For almost 35 years, Sch{\"o}nhage-Strassen's algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n $\times$ log n $\times$ log log n) for multiplying n-bit inputs. In 2007, F{\"u}rer proved that there exists
Covanov, Svyatoslav, Thomé, Emmanuel
core   +4 more sources

Primality deterministic and primality probabilistic tests

Statistica, 2007
In this paper the A. comments the importance of prime numbers in mathematics and in cryptography. He remembers the very important researches of Eulero, Fermat, Legen-re, Rieman and others scholarships.
Alfredo Rizzi
doaj   +1 more source

The Weighted Fermat Triangle Problem

International Journal of Mathematics and Mathematical Sciences, 2008
We completely solve the generalized Fermat problem: given a triangle 𝑃1, 𝑃2, 𝑃3 and three positive numbers 𝜆1, 𝜆2, 𝜆3, find a point 𝑃 for which the sum 𝜆1𝑃1𝑃+𝜆2𝑃2𝑃+𝜆3𝑃3𝑃 is minimal.
Yujin Shen, Juan Tolosa
doaj   +1 more source

The twentieth Fermat number is composite [PDF]

Mathematics of Computation, 1988
The twentieth Fermat number, F 20 = 2 2 20 + 1 {F_{20}
Young, Jeff, Buell, Duncan A.
openaire   +1 more source

Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices

Advances in Difference Equations, 2019
In this paper, we deal mainly with a class of periodic tridiagonal Toeplitz matrices with perturbed corners. By matrix decomposition with the Sherman–Morrison–Woodbury formula and constructing the corresponding displacement of matrices we derive the ...
Yunlan Wei, Xiaoyu Jiang, Zhaolin Jiang, Sugoog Shon   +3 more
doaj   +1 more source

Distribution of generalized Fermat prime numbers [PDF]

Mathematics of Computation, 2001
Summary: Numbers of the form \(F_{b,n}=b^{2^n}+1\) are called Generalized Fermat Numbers (GFN). A computational method for testing the probable primality of a GFN is described which is as fast as testing a number of the form \(2^m-1\). The theoretical distributions of GFN primes, for fixed \(n\), are derived and compared to the actual distributions ...
Dubner, Harvey, Gallot, Yves
openaire   +2 more sources