Results 181 to 190 of about 1,108 (208)
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Nature, 1922
IN my presidential address to Section A of the British Association, reprinted in NATURE (September 16), I stated that 137 was the least value of n for which the prime or composite character of 2n–1 was still undecided. Mr. W. W. Rouse Ball has pointed out to me that this is incorrect, as 2137–1 has been shown to be composite by M. A.
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IN my presidential address to Section A of the British Association, reprinted in NATURE (September 16), I stated that 137 was the least value of n for which the prime or composite character of 2n–1 was still undecided. Mr. W. W. Rouse Ball has pointed out to me that this is incorrect, as 2137–1 has been shown to be composite by M. A.
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Global Generalized Mersenne Numbers: Definition, Decomposition, and Generalized Theorems
SymmetryA new generalized definition of Mersenne numbers is proposed of the form an−a−1n, called global generalized Mersenne numbers and noted GMa,n with base a and exponent n positive integers. The properties are investigated for prime n and several theorems on
Vladimir Pletser
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Mersenne numbers as a difference of two Lucas numbers
Commentationes Mathematicae Universitatis Carolinae, 2023Summary: Let \((L_n)_{n\geq 0}\) be the Lucas sequence. We show that the Diophantine equation \(L_n-L_m=M_k\) has only the nonnegative integer solutions \((n,m,k)=(2,0,1)\), \((3,1,2)\), \((3,2,1)\), \((4,3,2)\), \((5,3,3)\), \((6,2,4)\), \((6,5,3)\) where \(M_k=2^k-1\) is the \(k\)th Mersenne number and \(n>m\).
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Search Limits on Divisors of Mersenne numbers
BIT, 1962On the urgent request of several coenthusiasts around the globe in the field of Factorization of Mersenne Numbers, the author publishes here for the first time the search limits on divisorsq of 2p − 1, even when no divisor up to this limit was found. This list, therefore, should avoid time consuming double work.
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New Vistas on Mersenne numbers
Proceeding International Conference on Science and Engineering, 2023Mersenne numbers are analyzed for varieties of interesting properties. Various fascinating relations connecting Mersenne numbers with other special number patterns by means of theorems involving the relations are exhibited.
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On Lucas's Test for the Primality of Mersenne's Numbers
Journal of the London Mathematical Society, 1935Beweis des Satzes: Ist \(p\) eine Primzahl \((\neq 2)\), so ist \(N = 2^p - 1\) dann und nur dann eine Primzahl, wenn das \((n - 1)\)-te Glied der Reihe \(S_1 = 4, \ldots, S_k= S_{k-1}^2 - 1\) teilbar ist durch \(N\). Ein Teil dieses Satzes ist von Lucas; sein Beweis war nicht einwandfrei. Verf. gebraucht die Reihe \(U_r =\frac{(a^r - b^r)}{(a - b)}\),
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On the generalization of Mersenne and Gaussian Mersenne polynomials
Journal of Analysis, 2023Munesh Kumari +2 more
exaly
Some Properties between Mersenne, Jacobsthal and Jacobsthal-Lucas Hybrid Numbers
Chaos, Solitons and Fractals, 2021Dursun Tasci, Emre Sevgi
exaly
Mersenne Numbers, Recursive Generation of Natural Numbers, and Counting the Number of Prime Numbers
Applied Mathematics, 2022Ramon Carbö-D̈Orca
exaly
On the bivariate Mersenne Lucas polynomials and their properties
Chaos, Solitons and Fractals, 2021Nabiha Saba, Ali Boussayoud
exaly