Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
http://hdl.handle.net/11320/3709
Pełny rekord metadanych
Pole DC | Wartość | Język |
---|---|---|
dc.contributor.author | Schwarzweller, Christoph | - |
dc.date.accessioned | 2015-12-09T20:40:51Z | - |
dc.date.available | 2015-12-09T20:40:51Z | - |
dc.date.issued | 2014 | - |
dc.identifier.citation | Formalized Mathematics, Volume 22, Issue 2, 2014, Pages 111-118 | - |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.issn | 1898-9934 | - |
dc.identifier.uri | http://hdl.handle.net/11320/3709 | - |
dc.description.abstract | In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime. | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.subject | prime numbers | - |
dc.subject | Pocklington’s theorem | - |
dc.subject | Proth’s theorem | - |
dc.subject | Pepin’s theorem | - |
dc.title | Proth Numbers | - |
dc.type | Article | - |
dc.identifier.doi | 10.2478/forma-2014-0013 | - |
dc.description.Affiliation | WSB Schools of Banking Gdańsk, Poland | - |
dc.description.references | Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990. | - |
dc.description.references | Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990. | - |
dc.description.references | J. Buchmann and V. Müller. Primality testing. 1992. | - |
dc.description.references | Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990. | - |
dc.description.references | Yoshinori Fujisawa, Yasushi Fuwa, and Hidetaka Shimizu. Public-key cryptography and Pepin’s test for the primality of Fermat numbers. Formalized Mathematics, 7(2):317–321, 1998. | - |
dc.description.references | Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, and Yasunari Shidama. Operations of points on elliptic curve in projective coordinates. Formalized Mathematics, 20(1):87–95, 2012. doi:10.2478/v10037-012-0012-2. | - |
dc.description.references | Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841–845, 1990. | - |
dc.description.references | Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887–890, 1990. | - |
dc.description.references | Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829–832, 1990. | - |
dc.description.references | Hiroyuki Okazaki and Yasunari Shidama. Uniqueness of factoring an integer and multiplicative group Z/pZ*. Formalized Mathematics, 16(2):103–107, 2008. doi:10.2478/v10037-008-0015-1. | - |
dc.description.references | Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335–338, 1997. | - |
dc.description.references | Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445–449, 1990. | - |
dc.description.references | Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501–505, 1990. | - |
dc.description.references | Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990. | - |
dc.description.references | Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990. | - |
dc.description.references | Li Yan, Xiquan Liang, and Junjie Zhao. Gauss lemma and law of quadratic reciprocity. Formalized Mathematics, 16(1):23–28, 2008. doi:10.2478/v10037-008-0004-4. | - |
Występuje w kolekcji(ach): | Formalized Mathematics, 2014, Volume 22, Issue 2 |
Pliki w tej pozycji:
Plik | Opis | Rozmiar | Format | |
---|---|---|---|---|
forma-2014-0013.pdf | 253,06 kB | Adobe PDF | Otwórz |
Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL