Results 11 to 20 of about 986 (177)

Generalised Mersenne numbers revisited [PDF]

Mathematics of Computation, 2013
32 pages.
Robert Granger, Andrew Moss
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A study on the number of edges of some families of graphs and generalized Mersenne numbers

Ratio Mathematica, 2022
The relationship between the Nandu sequence of the SM family of graphs and the Generalized Mersenne numbers is demonstrated in this study. Nandu sequences are related to the two families of SM sum graphs and SM Balancing graphs.
K.G. Sreekumar, Ramesh Kumar. P., K. Manilal, K. Manilal   +3 more
doaj   +1 more source

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
doaj   +1 more source

Radix-2² Algorithm for the Odd New Mersenne Number Transform (ONMNT)

Signals, 2023
This paper introduces a new derivation of the radix-22 fast algorithm for the forward odd new Mersenne number transform (ONMNT) and the inverse odd new Mersenne number transform (IONMNT).
Yousuf Al-Aali, Mounir T. Hamood, Said Boussakta   +2 more
doaj   +1 more source

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, Matthew Faust, A. J. Hildebrand, Junxian Li, Yuan Zhang   +4 more
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Non-negative Solutions of the Nonlinear Diophantine Equation (8^n)^x + p^y=z^2 for Some Prime Number p

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
doaj   +3 more sources

On digits of Mersenne numbers

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, László Mérai, Igor E. Shparlinski   +2 more
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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, Leomarich F Casinillo, Jorge S Valenzona, Divina L Valenzona   +3 more
doaj   +1 more source

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
doaj   +1 more source

The generalized order (k,t)-Mersenne sequences in groups [PDF]

Notes on Number Theory and Discrete Mathematics
The 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
doaj   +1 more source