Results 1 to 10 of about 973 (162)

On generalized bihyperbolic Mersenne numbers [PDF]

Mathematica Bohemica, 2023
In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained.
Dorota Bród, Anetta Szynal-Liana
doaj   +2 more sources

Features of digital signal processing algorithms using Galois fields GF(2n+1). [PDF]

PLoS ONE, 2023
An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1 ...
Ibragim E Suleimenov, Yelizaveta S Vitulyova, Dinara K Matrassulova   +2 more
doaj   +2 more sources

Learned pseudo-random number generator: WGAN-GP for generating statistically robust random numbers. [PDF]

PLoS ONE, 2023
Pseudo-random number generators (PRNGs) are software algorithms generating a sequence of numbers approximating the properties of random numbers. They are critical components in many information systems that require unpredictable and nonarbitrary ...
Kiyoshiro Okada, Katsuhiro Endo, Kenji Yasuoka, Shuichi Kurabayashi   +3 more
doaj   +2 more sources

The specifics of the Galois field GF(257) and its use for digital signal processing [PDF]

Scientific Reports
An algorithm of digital logarithm calculation for the Galois field $$GF(257)$$ G F ( 257 ) is proposed. It is shown that this field is coupled with one of the most important existing standards that uses a digital representation of the signal through 256 ...
Akhat Bakirov, Dinara Matrassulova, Yelizaveta Vitulyova, Dina Shaltykova, Ibragim Suleimenov   +4 more
doaj   +2 more sources

Mersenne version of Brocard-Ramanujan equation

Journal of New Results in Science, 2023
In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one of the interesting and still open problems of Diophantine analysis.
Ayşe Nalli, Seyran İbrahimov
doaj   +1 more source

Generalised Mersenne numbers revisited [PDF]

Mathematics of Computation, 2013
32 pages.
Robert Granger, Andrew Moss
openaire   +5 more sources

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

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