Genefer: Programs for Finding Large Probable Generalized Fermat Primes

Fast integer multiplication using generalized Fermat primes

Mathematics of Computation ◽

10.1090/mcom/3367 ◽

2018 ◽

Vol 88 (317) ◽

pp. 1449-1477

Author(s):

Svyatoslav Covanov ◽

Emmanuel Thomé

Keyword(s):

Integer Multiplication ◽

Fermat Primes

A characterization of symplectic groups related to Fermat primes

Commentationes Mathematicae Universitatis Carolinae ◽

10.14712/1213-7243.2020.033 ◽

2021 ◽

Vol 62 (1) ◽

pp. 33-40

Author(s):

Ebrahimzadeh Behnam ◽

Asboei Alireza K.

Keyword(s):

Symplectic Groups ◽

Fermat Primes

New Worlds to Conquer

Mathematics Teacher ◽

10.5951/mt.98.3.0166 ◽

2004 ◽

Vol 98 (3) ◽

pp. 166-170

Author(s):

Richard L. Francis

Keyword(s):

Problem Solving ◽

Mathematical Problem ◽

Prime Numbers ◽

Mathematical Problem Solving ◽

Fermat Primes

Still undiscovered areas of mathematical problem solving. Prime numbers and subset groups are discussed, including Mersenne and Fermat primes.

EQUIDISTRIBUTION OF DIVISORS IN RESIDUE CLASSES AND REPRESENTATIONS BY BINARY QUADRATIC FORMS

International Journal of Number Theory ◽

10.1142/s1793042113500711 ◽

2013 ◽

Vol 09 (08) ◽

pp. 2011-2018 ◽

Cited By ~ 1

Author(s):

MICHAEL DRMOTA ◽

MARIUSZ SKAŁBA

Keyword(s):

Quadratic Forms ◽

Binary Quadratic Form ◽

Binary Quadratic Forms ◽

Residue Classes ◽

Number Of Divisors ◽

Class 1 ◽

Combinatorial Technique ◽

Natural Density ◽

Almost All ◽

Fermat Primes

We study the number of divisors in residue classes modulo m and prove, for example, that the exact equidistribution holds for almost all natural numbers coprime to m in the sense of natural density if and only if m = 2kp1p2…ps, where k and s are non-negative integers and pj are distinct Fermat primes. We also provide a general and exact lower bound for the proportion of divisors in the residue class 1 mod m. The same combinatorial technique using Davenport's constant leads to exact lower bounds for the number of representations of a natural number by a given binary quadratic form with a negative discriminant.

High-radix transforms for Reed-Solomon codes over Fermat primes (Corresp.)

IEEE Transactions on Information Theory ◽

10.1109/tit.1977.1055786 ◽

1977 ◽

Vol 23 (6) ◽

pp. 776-778 ◽

Cited By ~ 2

Author(s):

Kwang Liu ◽

I. Reed ◽

Treiu-Kien Truong

Keyword(s):

Reed Solomon Codes ◽

High Radix ◽

Fermat Primes

Diophantine representation of Mersenne and Fermat primes

Acta Arithmetica ◽

10.4064/aa-35-3-209-221 ◽

1979 ◽

Vol 35 (3) ◽

pp. 209-221 ◽

Cited By ~ 13

Author(s):

James Jones

Keyword(s):

Diophantine Representation ◽

Fermat Primes

Parity patterns in Hecke groups and Fermat primes

Groups ◽

10.1017/cbo9780511550706.013 ◽

2004 ◽

pp. 327-374 ◽

Cited By ~ 2

Author(s):

T. W. Müller

Keyword(s):

Hecke Groups ◽

Fermat Primes

On the generating functions of Mersenne and Fermat primes

Collectanea mathematica ◽

10.1007/s13348-010-0019-3 ◽

2010 ◽

Vol 63 (1) ◽

pp. 59-69 ◽

Cited By ~ 1

Author(s):

Pablo A. Panzone

Keyword(s):

Generating Functions ◽

Fermat Primes

Room quasigroups and fermat primes

Journal of Algebra ◽

10.1016/0021-8693(72)90087-7 ◽

1972 ◽

Vol 20 (1) ◽

pp. 83-89 ◽

Cited By ~ 2

Author(s):

R.G Stanton ◽

R.C Mullin

Keyword(s):

Fermat Primes

Solvability by Real Radicals and Fermat Primes

Canadian Mathematical Bulletin ◽

10.4153/cmb-2004-022-9 ◽

2004 ◽

Vol 47 (2) ◽

pp. 229-236

Author(s):

C. U. Jensen

Keyword(s):

Real Number ◽

Number Field ◽

The Real ◽

Real Roots ◽

Fermat Primes ◽

Real Number Field

AbstractWe give a survey of old and new results concerning the expressibility of the real roots of a solvable polynomial over a real number field by real radicals. A characterization of Fermat primes is obtained in terms of solvability by real radicals for certain ploynomials.