Results 21 to 30 of about 1,108 (208)
Leading Digits of Mersenne Numbers [PDF]
Experimental Mathematics, 2019 It has long been known that sequences such as the powers of $2$ and the factorials satisfy Benford's Law; that is, leading digits in these sequences occur with frequencies given by $P(d)=\log_{10}(1+1/d)$, $d=1,2,\dots,9$. In this paper, we consider the leading digits of the Mersenne numbers $M_n=2^{p_n}-1$, where $p_n$ is the $n$-th prime. In light of
Zhaodong Cai +4 more
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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
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On the solution of the exponential Diophantine equation 2x+m2y=z2, for any positive integer m [PDF]
Journal of Hyperstructures, 2023 It is well known that the exponential Diophantine equation 2x+ 1=z2 has the unique solution x=3 and z=3 innon-negative integers, which is closely related to the Catlan's conjecture.
Mridul Dutta, Padma Bhushan Borah
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Mathematics of Computation, 1958 Im Jahre 1957 prüfte der Verf. mit Hilfe der Maschine BESK die Mersenneschen Zahlen \(M_p = 2^p-1\) für \(p < 10,000\). Und zwar zunächst alle diese auf etwaige Teiler \(< 10\cdot 2^{20}\) und hierauf diejenigen für \(2300 < p < 3300\), bei denen sich kein solcher Teiler ergab, nach dem Lucas-Test auf ihre Primheit. Dabei ergab sich nur \(2^{3217}- 1\)
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On the Split Mersenne and Mersenne-Lucas Hybrid Quaternions
مجلة بغداد للعلوم, 2023 In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.
B. Malini Devi, S. Devibala
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Cryptographically Strong Elliptic Curves of Prime Order [PDF]
International Journal of Electronics and Telecommunications, 2021 The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields Fp, where p is a Mersenne prime, one of the special primes or a random prime. We search for elliptic curves which orders are also prime numbers.
Marcin Barański +2 more
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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
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On the Lichtenberg hybrid quaternions [PDF]
Mathematica MoravicaIn this study, we define Lichtenberg hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formulas of these quaternions. We find some relations between Jacobsthal hybrid quaternions, Mersenne
Morales Gamaliel
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Nature, 1895 IN 1644 the mathematician Mersenne asserted that out of the 56 primes not < 257, there were only 12 primes, viz.:—
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مجلة بغداد للعلوم, 2023 In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test.
Yahia Awad, Ramiz Hindi, Haissam Chehade
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