REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU
UwB

Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/3709
Pełny rekord metadanych
Pole DCWartośćJęzyk
dc.contributor.authorSchwarzweller, Christoph-
dc.date.accessioned2015-12-09T20:40:51Z-
dc.date.available2015-12-09T20:40:51Z-
dc.date.issued2014-
dc.identifier.citationFormalized Mathematics, Volume 22, Issue 2, 2014, Pages 111-118-
dc.identifier.issn1426-2630-
dc.identifier.issn1898-9934-
dc.identifier.urihttp://hdl.handle.net/11320/3709-
dc.description.abstractIn 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.isoen-
dc.publisherDe Gruyter Open-
dc.subjectprime numbers-
dc.subjectPocklington’s theorem-
dc.subjectProth’s theorem-
dc.subjectPepin’s theorem-
dc.titleProth Numbers-
dc.typeArticle-
dc.identifier.doi10.2478/forma-2014-0013-
dc.description.AffiliationWSB Schools of Banking Gdańsk, Poland-
dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.-
dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91–96, 1990.-
dc.description.referencesJ. Buchmann and V. Müller. Primality testing. 1992.-
dc.description.referencesCzesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47–53, 1990.-
dc.description.referencesYoshinori 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.referencesYuichi 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.referencesAndrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841–845, 1990.-
dc.description.referencesRafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887–890, 1990.-
dc.description.referencesRafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relatively primes. Formalized Mathematics, 1(5):829–832, 1990.-
dc.description.referencesHiroyuki 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.referencesPiotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335–338, 1997.-
dc.description.referencesAndrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445–449, 1990.-
dc.description.referencesMichał J. Trybulec. Integers. Formalized Mathematics, 1(3):501–505, 1990.-
dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990.-
dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990.-
dc.description.referencesLi 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 RozmiarFormat 
forma-2014-0013.pdf253,06 kBAdobe PDFOtwórz
Pokaż uproszczony widok rekordu Zobacz statystyki


Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL Creative Commons