Elementary Number Theory Problems. Part II

Pole DC	Wartość	Język
dc.contributor.author	Korniłowicz, Artur	-
dc.contributor.author	Surowik, Dariusz	-
dc.date.accessioned	2021-08-30T09:33:43Z	-
dc.date.available	2021-08-30T09:33:43Z	-
dc.date.issued	2021	-
dc.identifier.citation	Formalized Mathematics, Volume 29, Issue 1, Pages 63-68	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/11413	-
dc.description.abstract	In this paper problems 14, 15, 29, 30, 34, 78, 83, 97, and 116 from [6] are formalized, using the Mizar formalism [1], [2], [3]. Some properties related to the divisibility of prime numbers were proved. It has been shown that the equation of the form p2 + 1 = q2 + r2, where p, q, r are prime numbers, has at least four solutions and it has been proved that at least five primes can be represented as the sum of two fourth powers of integers. We also proved that for at least one positive integer, the sum of the fourth powers of this number and its successor is a composite number. And finally, it has been shown that there are infinitely many odd numbers k greater than zero such that all numbers of the form 22n + k (n = 1, 2, . . . ) are composite.	pl
dc.language.iso	en	pl
dc.publisher	DeGruyter Open	pl
dc.rights	Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)	-
dc.rights.uri	https://creativecommons.org/licenses/by-sa/3.0/	-
dc.subject	number theory	pl
dc.subject	divisibility	pl
dc.subject	primes	pl
dc.title	Elementary Number Theory Problems. Part II	pl
dc.type	Article	pl
dc.rights.holder	© 2021 University of Białymstoku	pl
dc.rights.holder	CC-BY-SA License ver. 3.0 or later	pl
dc.identifier.doi	10.2478/forma-2021-0006	-
dc.description.Affiliation	Artur Korniłowicz - Institute of Informatics, University of Białystok, Poland	pl
dc.description.Affiliation	Dariusz Surowik - University of Białystok, Poland	pl
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8 17.	pl
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	pl
dc.description.references	Artur Korniłowicz. Flexary connectives in Mizar. Computer Languages, Systems & Structures, 44:238–250, December 2015. doi:10.1016/j.cl.2015.07.002.	pl
dc.description.references	Marco Riccardi. Pocklington’s theorem and Bertrand’s postulate. Formalized Mathematics, 14(2):47–52, 2006. doi:10.2478/v10037-006-0007-y.	pl
dc.description.references	Marco Riccardi. Solution of cubic and quartic equations. Formalized Mathematics, 17(2): 117–122, 2009. doi:10.2478/v10037-009-0012-z.	pl
dc.description.references	Wacław Sierpinski. 250 Problems in Elementary Number Theory. Elsevier, 1970.	pl
dc.identifier.eissn	1898-9934	-
dc.description.volume	29	pl
dc.description.issue	1	pl
dc.description.firstpage	63	pl
dc.description.lastpage	68	pl
dc.identifier.citation2	Formalized Mathematics	pl
dc.identifier.orcid	0000-0002-4565-9082	-
dc.identifier.orcid	0000-0003-2288-8138	-
Występuje w kolekcji(ach):	Artykuły naukowe (WFiloz) Artykuły naukowe (WInf) Formalized Mathematics, 2021, Volume 29, Issue 1

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