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  4. Formalized Mathematics, 2025, Volume 33, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/19736
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    Pole DCWartośćJęzyk
    dc.contributor.authorZiobro, Rafał-
    dc.date.accessioned2026-02-02T11:37:25Z-
    dc.date.available2026-02-02T11:37:25Z-
    dc.date.issued2025-
    dc.identifier.citationFormalized Mathematics, Volume 33, Issue 1, Pages 207-216pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/19736-
    dc.description.abstractThe paper illustrates how the formal framework proposed earlier for complex numbers can be applied to integer and natural numbers, facilitating proofs by means of clusters’ registrations for Mizar adjectives. The contents of the article are closely related to the series of Mizar articles “Elementary Number Theory Problems” (with MML identifiers NUMBER*), but it is not solving any of “250 Problems in Elementary Number Theory” by Wacław Sierpiński book.pl
    dc.language.isoenpl
    dc.publisherUniversity of Białystokpl
    dc.rightsAttribution-ShareAlike 4.0 International (CC BY-SA 4.0)pl
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/pl
    dc.subjectinteger numberspl
    dc.subjectmultiplicationpl
    dc.subjectdivisionpl
    dc.subjectroundingpl
    dc.titleApplication of Complex Classes to Number Theorypl
    dc.typeArticlepl
    dc.rights.holder2025 The Author(s)pl
    dc.rights.holderCC BY-SA 4.0 licensepl
    dc.identifier.doi10.2478/forma-2025-0016-
    dc.description.AffiliationDepartment of Carbohydrate Technology and Cereal Processing, University of Agriculture, Kraków, Polandpl
    dc.description.referencesGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. 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.referencesMarco B. Caminati and Giuseppe Rosolini. Custom automations in Mizar. Journal of Automated Reasoning, 50(2):147–160, 2013.pl
    dc.description.referencesAdam Grabowski and Artur Korniłowicz. Implementing more explicit definitional expansions in Mizar. In Adam Naumowicz and Rene Thiemann, editors, 14th International Conference on Interactive Theorem Proving, ITP 2023, Białystok, Poland, July 31–August 4, 2023, volume 268 of LIPIcs, pages 37:1–37:8. Schloss Dagstuhl – Leibniz-Zentrum fur Informatik, 2023. doi:10.4230/LIPICS.ITP.2023.37.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. Tentative experiments with ellipsis in Mizar. In Johan Jeuring, John A. Campbell, Jacques Carette, Gabriel Dos Reis, Petr Sojka, Makarius Wenzel, and Volker Sorge, editors, Intelligent Computer Mathematics, pages 453–457. Springer Berlin Heidelberg, 2012. doi:10.1007/978-3-642-31374-5 35.pl
    dc.description.referencesArtur Korniłowicz. Elementary number theory problems. Part III. Formalized Mathematics, 30(2):135–158, 2022. doi:10.2478/forma-2022-0011.pl
    dc.description.referencesArtur Korniłowicz. On rewriting rules in Mizar. Journal of Automated Reasoning, 50(2): 203–210, 2013.pl
    dc.description.referencesAdam Naumowicz. Elementary number theory problems. Part I. Formalized Mathematics, 28(1):115–120, 2020. doi:10.2478/forma-2020-0010.pl
    dc.description.referencesAdam Naumowicz. Dataset description: Formalization of elementary number theory in Mizar. In Christoph Benzmuller 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.referencesWacław Sierpiński. Elementary Theory of Numbers. PWN, Warsaw, 1964.pl
    dc.description.referencesWacław Sierpiński. Teoria liczb. Instytut Matematyczny Polskiej Akademii Nauk, 1950. In Polish.pl
    dc.description.referencesWacław Sierpiński. 250 Problems in Elementary Number Theory. Elsevier, 1970.pl
    dc.description.referencesJames J. Tattersall. The Intriguing Natural Numbers. Cambridge University Press, 2005.pl
    dc.description.referencesRafał Ziobro. Multiplication-related classes of complex numbers. Formalized Mathematics, 28(2):197–210, 2020. doi:10.2478/forma-2020-0017.pl
    dc.description.referencesRafał Ziobro. Some remarkable identities involving numbers. Formalized Mathematics, 22(3):205–208, 2014. doi:10.2478/forma-2014-0023.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.description.referencesRafał Ziobro. Parity as a property of integers. Formalized Mathematics, 26(2):91–100, 2018. doi:10.2478/forma-2018-0008.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume33pl
    dc.description.issue1pl
    dc.description.firstpage207pl
    dc.description.lastpage216pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0001-9681-4380-
    Występuje w kolekcji(ach):Formalized Mathematics, 2025, Volume 33, Issue 1

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