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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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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
exaly
Some Properties between Mersenne, Jacobsthal and Jacobsthal-Lucas Hybrid Numbers
Chaos, Solitons and Fractals, 2021Dursun Taşci̧, Emre Sevgi
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On the bivariate Mersenne Lucas polynomials and their properties
Chaos, Solitons and Fractals, 2021Ali Boussayoud, Nabiha Saba
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On the Norms and Eigenvalues of rr-Circulant Matrices with kk-Mersenne and kk-Mersenne–Lucas Numbers
Mathematical Notes, 2023Jagmohan Tanti +2 more
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