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  4. Formalized Mathematics, 2023, Volume 31, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/15860
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    Pole DCWartośćJęzyk
    dc.contributor.authorGrabowski, Adam-
    dc.date.accessioned2024-01-26T08:14:49Z-
    dc.date.available2024-01-26T08:14:49Z-
    dc.date.issued2023-
    dc.identifier.citationFormalized Mathematics, Volume 31, Issue 1, Pages 277-286pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/15860-
    dc.description.abstractIn this paper another twelve problems from W. Sierpiński’s book “250 Problems in Elementary Number Theory” are formalized, using the Mizar formalism, namely: 42, 43, 51, 51a, 57, 59, 72, 135, 136, and 153–155. Significant amount of the work is devoted to arithmetic progressions.pl
    dc.language.isoenpl
    dc.publisherDeGruyter Openpl
    dc.rightsAttribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)pl
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/3.0/pl
    dc.subjectnumber theorypl
    dc.subjectprimespl
    dc.subjectarithmetic progressionpl
    dc.titleElementary Number Theory Problems. Part XII – Primes in Arithmetic Progressionpl
    dc.typeArticlepl
    dc.rights.holder© 2022 The Author(s)pl
    dc.rights.holderCC BY-SA 3.0 licensepl
    dc.identifier.doi10.2478/forma-2023-0022-
    dc.description.AffiliationFaculty of Computer Science, University of Białystok, Polandpl
    dc.description.referencesLeonard Eugene Dickson. History of Theory of Numbers. New York, 1952.pl
    dc.description.referencesAdam Grabowski. Elementary number theory problems. Part VI. Formalized Mathematics, 30(3):235–244, 2022. doi:10.2478/forma-2022-0019.pl
    dc.description.referencesAdam Grabowski. Polygonal numbers. Formalized Mathematics, 21(2):103–113, 2013. doi:10.2478/forma-2013-0012.pl
    dc.description.referencesAdam Grabowski and Christoph Schwarzweller. Translating mathematical vernacular into knowledge repositories. In Michael Kohlhase, editor, Mathematical Knowledge Management, volume 3863 of Lecture Notes in Computer Science, pages 49–64. Springer, 2006. doi:10.1007/11618027 4. 4th International Conference on Mathematical Knowledge Management, Bremen, Germany, MKM 2005, July 15–17, 2005, Revised Selected Papers.pl
    dc.description.referencesAdam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Mizar in a nutshell. Journal of Formalized Reasoning, 3(2):153–245, 2010.pl
    dc.description.referencesArtur 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.referencesArtur Korniłowicz and Adam Naumowicz. Elementary number theory problems. Part V. Formalized Mathematics, 30(3):229–234, 2022. doi:10.2478/forma-2022-0018.pl
    dc.description.referencesAdam Naumowicz. Dataset description: Formalization of elementary number theory in Mizar. In Christoph Benzmüller and Bruce R. Miller, editors, Intelligent Computer Mathematics – 13th International Conference, CICM 2020, Bertinoro, Italy, July 26–31, 2020, Proceedings, volume 12236 of Lecture Notes in Computer Science, pages 303–308. Springer, 2020. doi:10.1007/978-3-030-53518-6_22.pl
    dc.description.referencesAdam Naumowicz. Extending numeric automation for number theory formalizations in Mizar. In Catherine Dubois and Manfred Kerber, editors, Intelligent Computer Mathematics – 16th International Conference, CICM 2023, Cambridge, UK, September 5–8, 2023, Proceedings, volume 14101 of Lecture Notes in Computer Science, pages 309–314. Springer, 2023. doi:10.1007/978-3-031-42753-4_23.pl
    dc.description.referencesChristoph Schwarzweller. Proth numbers. Formalized Mathematics, 22(2):111–118, 2014. doi:10.2478/forma-2014-0013.pl
    dc.description.referencesWacław Sierpiński. Elementary Theory of Numbers. PWN, Warsaw, 1964.pl
    dc.description.referencesWacław Sierpiński. 250 Problems in Elementary Number Theory. Elsevier, 1970.pl
    dc.description.referencesNguyen Xuan Tho. On a remark of Sierpiński. Rocky Mountain Journal of Mathematics, 52(2):717–726, 2022. doi:10.1216/rmj.2022.52.717.pl
    dc.description.referencesRafał Ziobro. Fermat’s Little Theorem via divisibility of Newton’s binomial. Formalized Mathematics, 23(3):215–229, 2015. doi:10.1515/forma-2015-0018.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume31pl
    dc.description.issue1pl
    dc.description.firstpage277pl
    dc.description.lastpage286pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0001-5026-3990-
    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2023, Volume 31, Issue 1

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