Results 21 to 30 of about 524 (199)
On recognition of simple group L2(r) by the number of Sylow subgroups
Acta Scientiarum: Technology, 2014 Let G be a finite group and n_{p}(G) be the number of Sylow p- subgroup of G. In this work it is proved if G is a centerless group and n_{p}(G)=n_{p}(L_{2}(r)), for every prime p in pi (G), where r is prime number, r^2 does not divide |G| and r is not ...
Alireza Khalili Asboei +1 more
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A framework for cryptographic problems from linear algebra
Journal of Mathematical Cryptology, 2020 We introduce a general framework encompassing the main hard problems emerging in lattice-based cryptography, which naturally includes the recently proposed Mersenne prime cryptosystem, but also problems coming from code-based cryptography.
Bootland Carl +3 more
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Autocorrelation and Lower Bound on the 2-Adic Complexity of LSB Sequence of
IEEE Access, 2020 LSB (Least Significant Bit) sequences are widely used as the initial inputs in some modern stream ciphers, such as the ZUC algorithm-the core of the 3GPP LTE International Encryption Standard. Therefore, analyzing the statistical properties (for example,
Yuhua Sun +3 more
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Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II [PDF]
Notes on Number Theory and Discrete MathematicsLet ρ be an odd prime ≥ 11. In Part I, starting from an M-cycle in a finite field 𝔽_ρ, we have established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
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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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Mersenne Primes in Certain Lucas Sequences [PDF]
EPJ Web of ConferencesPrime numbers are the most important numbers in number theory and cryptography. One of such special primes are given by the set of Mersenne primes, that are derived from the form Mn = 2n − 1, where n is a prime number.
Hadi Ahmed H., Hashim Hayder R.
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Computer Experiments with Mersenne Primes [PDF]
Computational Methods in Science and Technology, 2013 We have calculated on the computer the sum $\bar{\BB}_M$ of reciprocals of all 47 known Mersenne primes with the accuracy of over 12000000 decimal digits. Next we developed $\bar{\BB}_M$ into the continued fraction and calculated geometrical means of the partial denominators of the continued fraction expansion of $\bar{\BB}_M$. We get values converging
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On digits of Mersenne numbers [PDF]
, 2022 Motivated by recently developed interest to the distribution of $q$-arydigits of Mersenne numbers $M_p = 2^p-1$, where $p$ is prime, we estimaterational exponential sums with $M_p$, $p \leq X$, modulo a large power of afixed odd prime $q$.
Shparlinski, I. +2 more
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Random number generators with period divisible by a Mersenne prime
, 2003 Colloque avec actes et comité de lecture. internationale.International audiencePseudo-random numbers with long periods and good statistical properties are often required for applications in computational finance.
Brent, Richard, P., Zimmermann, Paul
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ON THE LARGEST PRIME FACTOR OF THE MERSENNE NUMBERS [PDF]
Bulletin of the Australian Mathematical Society, 2009 AbstractLetP(k) be the largest prime factor of the positive integerk. In this paper, we prove that the seriesis convergent for each constantα<1/2, which gives a more precise form of a result of C. L. Stewart [‘On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers’,Proc. London Math. Soc.35(3) (1977), 425–447].
Ford, Kevin +2 more
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