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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 2nā1 was still undecided. Mr. W. W. Rouse Ball has pointed out to me that this is incorrect, as 2137ā1 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 2nā1 was still undecided. Mr. W. W. Rouse Ball has pointed out to me that this is incorrect, as 2137ā1 has been shown to be composite by M. A.
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SOME IDENTITIES OF k-MERSENNE NUMBERS
Advances and Applications in Discrete Mathematics, 2017Summary: In this study, we first examine \(k\)-Mersenne numbers. Then we obtain some identities on the \(k\)-Mersenne numbers.
Uslu, Kemal, Deniz, Vural
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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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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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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 ā 1, even when no divisor up to this limit was found. This list, therefore, should avoid time consuming double work.
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Mersenne Numbers in Generalized Lucas Sequences
Proceedings of the Bulgarian Academy of SciencesLet $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer.
ALAN, Murat, Altassan, Alaa
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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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A Problem Connected with Mersenne's Numbers
The American Mathematical Monthly, 1902(1902). A Problem Connected with Mersenne's Numbers. The American Mathematical Monthly: Vol. 9, No. 2, pp. 34-36.
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On the generalization of Mersenne and Gaussian Mersenne polynomials
Journal of Analysis, 2023Jagmohan Tanti +2 more
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