Results 21 to 30 of about 8,606,543 (158)
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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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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Walailak Journal of Science and Technology, 2021 In this paper, we explain all non-negative integer solutions for the nonlinear Diophantine equation of type 8x + py = z2 when p is an arbitrary odd prime number and incongruent with 1 modulo 8.
Boorapa SINGHA
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On Triangular Secure Domination Number
InPrime, 2020 Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m)
Emily L Casinillo +3 more
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The generalized order (k,t)-Mersenne sequences in groups [PDF]
Notes on Number Theory and Discrete MathematicsThe purpose of this paper is to determine the algebraic properties of finite groups via a Mersenne-like sequence. Firstly, we introduce the generalized order (k,t)-Mersenne number sequences and study the periods of these sequences modulo m.
E. Mehraban, Ö. Deveci, E. Hincal
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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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High performance FPGA implementation of the mersenne twister [PDF]
, 2008 Efficient generation of random and pseudorandom sequences is of great importance to a number of applications [4]. In this paper, an efficient implementation of the Mersenne Twister is presented. The proposed architecture has the smallest footprint of all
Shrutisagar Chandrasekaran +3 more
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HMNT: Hash Function Based on New Mersenne Number Transform
IEEE Access, 2020 In the field of information security, hash functions are considered important as they are used to ensure message integrity and authentication. Despite various available methods to design hash functions, the methods have been proven to time inefficient ...
Ali Maetouq, Salwani Mohd Daud
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Revista Matemática Iberoamericana, 2021 Motivated by recently developed interest to the distribution of q -ary digits of Mersenne numbers M_p = 2^p-1 , where p
Bryce Kerr +2 more
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Nature, 1911 I DESIRE to announce the discovery which I have made that (2181 —;1) is divisible by 43441. This leaves only 16 of the numbers (2q — 1) originally reported composite by Mersenne, still unverified. I have submitted my determination to Lt.—Col. Allan Cunningham, R.E., who has kindly verified it.
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