A necessary and sufficient condition for the primality of Fermat numbers

Title:

A necessary and sufficient condition for the primality of Fermat numbers

Creator:

Křížek, Michal and Somer, Lawrence

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:9a7e2204-219e-49ed-b6db-47bd766cc0ad
uuid:9a7e2204-219e-49ed-b6db-47bd766cc0ad

Subject:

Fermat numbers, primitive roots, primality, and Sophie Germain primes

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We examine primitive roots modulo the Fermat number Fm = 2 2m + 1. We show that an odd integer n ≥ 3 is a Fermat prime if and only if the set of primitive roots modulo n is equal to the set of quadratic non-residues modulo n. This result is extended to primitive roots modulo twice a Fermat number.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

541-549

Source:

Mathematica bohemica | 2001 Volume:126 | Number:3

Harvested from:

CDK

Metadata only:

false