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LAX1 as a core biomarker in Alzheimer's disease and periodontitis via the STAT signaling pathway. [PDF]
Guo H +6 more
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Integrity verified lightweight ciphering for secure medical image sharing between embedded SoCs. [PDF]
Janakiraman S +5 more
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Pushing the boundary of quantum advantage in hard combinatorial optimization with probabilistic computers. [PDF]
Chowdhury S +14 more
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Development and Internal Validation of a Prediction Model for Major Cardiovascular and Respiratory Events in Chronic Obstructive Pulmonary Disease: Nationwide Primary Care Electronic Medical Records Cohort Study. [PDF]
Gale CP +14 more
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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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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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