Results 1 to 10 of about 12,326 (180)
BiEntropy, TriEntropy and Primality [PDF]
Entropy, 2020 The order and disorder of binary representations of the natural numbers < 28 is measured using the BiEntropy function. Significant differences are detected between the primes and the non-primes.
Grenville J. Croll
doaj +2 more sources
Fermat numbers and Fibonacci numbers on Heron triangles [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 We mainly give necessary and sufficient conditions for being a Heron triangle in the case of certain classes of an isosceles triangles with the three sides (𝑎, 𝑎, 𝑐), where 𝑐 is an arbitrary positive integer, and 𝑎 is a Fermat or Fibonacci prime.
Chinnawat Tangkanchanawong +1 more
doaj +1 more source
Fermat $k$-Fibonacci and $k$-Lucas numbers [PDF]
Mathematica Bohemica, 2020 Using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and Pethő, we find all $k$-Fibonacci and $k$-Lucas numbers which are Fermat numbers.
Jhon J. Bravo, Jose L. Herrera
doaj +1 more source
Fermat and Mersenne numbers in $k$-Pell sequence
Математичні Студії, 2021 For an integer $k\geq 2$, let $(P_n^{(k)})_{n\geq 2-k}$ be the $k$-generalized Pell sequence, which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is defined by the recurrence $ P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}
B. Normenyo, S. Rihane, A. Togbe
doaj +1 more source
On the Properties of r-Circulant Matrices Involving Generalized Fermat Numbers
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 -circulant matrices have applied in numerical computation, signal processing, coding theory, etc. In this study, our main goal is to investigate the r-circulant matrices of generalized Fermat numbers which are shown by We obtain the eigenvalues ...
Engin Özkan, Engin Eser, Bahar Kuloǧlu
doaj +1 more source
Mathematics, 2022 The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients for a specific z.
Waleed Mohamed Abd-Elhameed +2 more
doaj +1 more source
Fermat Numbers and Mersenne Numbers [PDF]
Mathematics of Computation, 1964 This paper gives details of the computations made on an IBM 7090 computer to show that the Fermat number \(F_m = 2^{2^m} +1\) is composite for \(m=14\), and that all the Mersenne numbers \(M_p=2^p-1\) \((5000 < p < 6000)\) are composite. The method used to show that the Fermat number is composite was to compute \(3^{2^n}\) modulo \(F_m\).
Selfridge, J. L., Hurwitz, Alexander
openaire +2 more sources
Minimality Conditions Equivalent to the Finitude of Fermat and Mersenne Primes
Axioms, 2023 The question is still open as to whether there exist infinitely many Fermat primes or infinitely many composite Fermat numbers. The same question concerning Mersenne numbers is also unanswered.
Menachem Shlossberg
doaj +1 more source
Design Method of Freeform Off-Axis Multi-Mirror Optical Systems
Photonics, 2022 A data point calculation method that does not require the use of Fermat′s principle and a simple and general design method of starting points of freeform off-axis multi-mirror optical systems are proposed in this paper, which aim to promote the ...
Xinyu Liu, Jun Zhu
doaj +1 more source
Factors of Generalized Fermat Numbers [PDF]
Mathematics of Computation, 1995 Generalized Fermat numbers have the form F b , m = b 2 m + 1 {F_ ...
Dubner, Harvey, Keller, Wilfrid
openaire +1 more source