scholarly journals Algorithm Available for Factoring Big Fermat Numbers

2020 ◽  
pp. 86-97
Author(s):  
Xingbo Wang ◽  
Keyword(s):  
Fermat Numbers

scholarly journals Parallel Strategy to Factorize Fermat Numbers with Implementation in Maple Software

2021 ◽  
pp. 167-173
Author(s):  
Jianhui Li ◽  
◽  
Manlan Liu
Keyword(s):  
Parallel Computing ◽  
Parallel Algorithm ◽  
Computational Efficiency ◽  
Sequential Algorithm ◽  
Parallel Processes ◽  
Fermat Numbers ◽  
Fermat Number ◽  
Parallel Strategy

In accordance with the traits of parallel computing, the paper proposes a parallel algorithm to factorize the Fermat numbers through parallelization of a sequential algorithm. The kernel work to parallelize a sequential algorithm is presented by subdividing the computing interval into subintervals that are assigned to the parallel processes to perform the parallel computing. Maple experiments show that the parallelization increases the computational efficiency of factoring the Fermat numbers, especially to the Fermat number with big divisors.

scholarly journals Four new factors of Fermat numbers

1978 ◽  
Vol 32 (143) ◽  
pp. 941 ◽  
Author(s):  
D. E. Shippee
Keyword(s):  
Fermat Numbers

Primality of Fermat Numbers

2002 ◽  
pp. 41-58
Author(s):  
Michal Křížek ◽  
Florian Luca ◽  
Lawrence Somer
Keyword(s):  
Fermat Numbers

A Curious Connection between Fermat Numbers and Finite Groups

2002 ◽  
Vol 109 (6) ◽  
pp. 517 ◽  
Author(s):  
Carrie E. Finch ◽  
Lenny Jones
Keyword(s):  
Finite Groups ◽  
Fermat Numbers

scholarly journals On the multiplicative order of elements in Wiedemann's towers of finite fields

2015 ◽  
Vol 7 (2) ◽  
pp. 220-225
Author(s):  
R. Popovych
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Field Extensions ◽  
Fermat Numbers ◽  
Multiplicative Order ◽  
Order Of Elements

We consider recursive binary finite field extensions $E_{i+1} =E_{i} (x_{i+1} )$, $i\ge -1$, defined by D. Wiedemann. The main object of the paper is to give some proper divisors of the Fermat numbers $N_{i} $ that are not equal to the multiplicative order $O(x_{i} )$.

scholarly journals Table errata 2 to “Factors of generalized Fermat numbers”

2010 ◽  
Vol 80 (275) ◽  
pp. 1865-1866
Author(s):  
Anders Björn ◽  
Hans Riesel
Keyword(s):  
Fermat Numbers

Basic Properties of Fermat Numbers

2002 ◽  
pp. 26-32
Author(s):  
Michal Křížek ◽  
Florian Luca ◽  
Lawrence Somer
Keyword(s):  
Basic Properties ◽  
Fermat Numbers
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