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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/11320/19732
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    Pole DCWartośćJęzyk
    dc.contributor.authorKorniłowicz, Artur-
    dc.contributor.authorNaumowicz, Adam-
    dc.date.accessioned2026-02-02T08:30:39Z-
    dc.date.available2026-02-02T08:30:39Z-
    dc.date.issued2025-
    dc.identifier.citationFormalized Mathematics, Volume 33, Issue 1, Pages 145-164pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/19732-
    dc.description.abstractThis paper furthers the formalization of problems from Wacław Sierpiński book “250 Problems in Elementary Number Theory” in the Mizar system. The selected twelve items are 37, 101, 115, 117, 145, 157, 159, 161–163, 165, and 169.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.subjectnumber theorypl
    dc.subjectprime numberpl
    dc.subjectfinite sequencepl
    dc.titleElementary Number Theory Problems. Part XVIIpl
    dc.typeArticlepl
    dc.rights.holder2025 The Author(s)pl
    dc.rights.holderCC BY-SA 4.0 licensepl
    dc.identifier.doi10.2478/forma-2025-0012-
    dc.description.AffiliationArtur Korniłowicz - Faculty of Computer Science, University of Białystok, Polandpl
    dc.description.AffiliationAdam Naumowicz - Faculty of Computer Science, University of Białystok, Polandpl
    dc.description.referencesGrzegorz Bancerek. On multiset ordering. Formalized Mathematics, 24(2):95–106, 2016. doi:10.1515/forma-2016-0008.pl
    dc.description.referencesJohn Horton Conway and R.K. Guy. The Book of Numbers. Springer-Verlag, 1996.pl
    dc.description.referencesLeonard Eugene Dickson. History of Theory of Numbers. New York, 1952.pl
    dc.description.referencesHarvey Dubner and Wilfrid Keller. Factors of generalized Fermat numbers. Mathematics of Computation, 64(209):397–405, 1995. doi:10.2307/2153343.pl
    dc.description.referencesMichael Filaseta and Jeremiah Southwick. Primes that become composite after changing an arbitrary digit. Mathematics of Computation, 90:979–993, 2021.doi:10.1090/mcom/3593.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. Cauchy mean theorem. Formalized Mathematics, 22(2):157–166, 2014.doi:10.2478/forma-2014-0016.pl
    dc.description.referencesAdam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.pl
    dc.description.referencesJon Grantham. Finding a widely digitally delicate prime. Integers, 23:#A22, 2023.doi:10.5281/zenodo.7692139.pl
    dc.description.referencesRichard K. Guy. Unsolved Problems in Number Theory. Problem Books in Mathematics.Springer, third edition, 2004. doi:10.1007/978-0-387-26677-0.pl
    dc.description.referencesDattathreya Ramachandra Kaprekar. Multidigital numbers. Scripta Mathematica, 21:27, 1955.pl
    dc.description.referencesArtur Korniłowicz. Elementary number theory problems. Part VII. Formalized Mathematics, 31(1):23–29, 2023. doi:10.2478/forma-2023-0003.pl
    dc.description.referencesMichal Krizek, Florian Luca, and Lawrence Somer. Factors of Fermat numbers. In 17 Lectures on Fermat Numbers: From Number Theory to Geometry, pages 70–79. Springer New York, 2001. doi:10.1007/978-0-387-21850-2_7.pl
    dc.description.referencesLouis J. Mordell. Diophantine Equations. Academic Press, 1969.pl
    dc.description.referencesAdam Naumowicz. Elementary number theory problems. Part XI. Formalized Mathematics, 31(1):229–275, 2023. doi:10.2478/forma-2023-0021.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.referencesKarol Pąk and Artur Korniłowicz. Elementary number theory problems. Part XV – Diophantine equations. Formalized Mathematics, 32(1):93–110, 2024. doi:10.2478/forma-2024-0007.pl
    dc.description.referencesColin Rothgang, Artur Korniłowicz, and Florian Rabe. A new export of the Mizar Mathematical Library. In Fairouz Kamareddine and Claudio Sacerdoti Coen, editors, Intelligent Computer Mathematics, pages 205–210, Cham, 2021. Springer International Publishing. doi:10.1007/978-3-030-81097-9_17.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. Sur les nombres compos´es de la forme a^2n+ 1. Colloquium Mathematicum, 10(1):133–135, 1963. doi:10.4064/cm-10-1-133-135.pl
    dc.description.referencesWacław Sierpiński. 250 Problems in Elementary Number Theory. Elsevier, 1970.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume33pl
    dc.description.issue1pl
    dc.description.firstpage145pl
    dc.description.lastpage164pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0002-4565-9082-
    dc.identifier.orcid0000-0003-4224-9798-
    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2025, Volume 33, Issue 1

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