On digits of Mersenne numbers

2021 ◽  
Author(s):  
Bryce Kerr ◽  
László Mérai ◽  
Igor Shparlinski
Keyword(s):  
Mersenne Numbers

scholarly journals Note on Mersenne numbers

1932 ◽  
Vol 38 (6) ◽  
pp. 383-385 ◽  
Author(s):  
D. H. Lehmer
Keyword(s):  
Mersenne Numbers

scholarly journals New factors of Mersenne numbers

1961 ◽  
Vol 15 (73) ◽  
pp. 51-51 ◽  
Author(s):  
Edgar Karst
Keyword(s):  
Mersenne Numbers

scholarly journals On the square-freeness of Fermat and Mersenne numbers

1967 ◽  
Vol 22 (3) ◽  
pp. 563-564 ◽  
Author(s):  
Leroy Warren ◽  
Henry Bray
Keyword(s):  
Mersenne Numbers

FERMAT AND MERSENNE NUMBERS IN PEPIN'S TEST1

2006 ◽  
Vol 39 (4) ◽  
Author(s):  
Alena Šolcová ◽  
Michał Křižek
Keyword(s):  
Mersenne Numbers

scholarly journals Lucas’ test for Mersenne numbers, $6000

1964 ◽  
Vol 18 (85) ◽  
pp. 148-148
Author(s):  
Sidney Kravitz ◽  
Murray Berg
Keyword(s):  
Mersenne Numbers

Lucas's Tests for Mersenne Numbers

1945 ◽  
Vol 52 (4) ◽  
pp. 188 ◽  
Author(s):  
Irving Kaplansky
Keyword(s):  
Mersenne Numbers

scholarly journals A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 893
Author(s):  
Yunlan Wei ◽  
Yanpeng Zheng ◽  
Zhaolin Jiang ◽  
Sugoog Shon
Keyword(s):  
Toeplitz Matrices ◽  
Schur Complement ◽  
Matrix Transformations ◽  
Matrix Decompositions ◽  
Mersenne Numbers

In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit determinants and inverses of these matrices. One feature of these formulas is the connection with the famous Mersenne numbers. We also propose two algorithms to illustrate our formulas.

scholarly journals Divisors of Mersenne numbers

1983 ◽  
Vol 40 (161) ◽  
pp. 385-385 ◽  
Author(s):  
Samuel S. Wagstaff
Keyword(s):  
Mersenne Numbers
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