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Type of publication: | Article |
Entered by: | ADM |
Title | Elitné prvočísla |
English Title | Elite Primes |
MESC | |
Bibtex cite ID | |
Journal | Obzory matematiky, fyziky a informatiky |
Year published | 2006 |
Volume | 35 |
Number | 4 |
Pages | 1-6 |
ISSN | 1335-4981 |
Abstract | A prime number p is called elite, if only finitely many Fermat numbers
Fm = 2^2^m +1 are quadratic residues modulo p. In this paper we give a survey on these
primes. In particular, we show how to prove that 3, 5, 7, and 41 are elite primes. Then
we introduce a necessary and sufficient condition for a prime to be elite. This condition
was recently used to determine all elite primes up to 25 ·10^10 on computers. They can
be applied as bases in the famous Pepin’s test. Several open problems concerning elite
primes are presented as well. |
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BibTeX | BibTeX |
RIS | RIS |
Total mark: | 5 |
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