{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T11:05:05Z","timestamp":1774868705178,"version":"3.50.1"},"reference-count":20,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,9,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>In this paper another seven problems from Wac\u0142aw Sierpi\u0144ski\u2019s book \u201c250 Problems in Elementary Number Theory\u201d are formalized, using the Mizar formalism, namely: 53, 61, 81, 90, 100, 156, and 167.<\/jats:p>","DOI":"10.2478\/forma-2025-0017","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T16:26:23Z","timestamp":1767975983000},"page":"217-229","source":"Crossref","is-referenced-by-count":0,"title":["Elementary Number Theory Problems. Part XVIII"],"prefix":"10.2478","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5026-3990","authenticated-orcid":false,"given":"Adam","family":"Grabowski","sequence":"first","affiliation":[{"name":"Faculty of Computer Science , University of Bia\u0142ystok , Poland"}]}],"member":"374","published-online":{"date-parts":[[2025,12,31]]},"reference":[{"key":"2026033010152199300_j_forma-2025-0017_ref_001","doi-asserted-by":"crossref","unstructured":"Kenichi Arai and Hiroyuki Okazaki. Properties of primes and multiplicative group of a field. Formalized Mathematics, 17(2):151\u2013155, 2009. doi:10.2478\/v10037-009-0017-7.","DOI":"10.2478\/v10037-009-0017-7"},{"key":"2026033010152199300_j_forma-2025-0017_ref_002","doi-asserted-by":"crossref","unstructured":"P.T. Bateman, J.L. Selfridge, and S.S. Wagsta Jr. The editor\u2019s corner: The new Mersenne conjecture. The American Mathematical Monthly, 96(2):125\u2013128, 1989. doi:10.1080\/00029890.1989.11972155.","DOI":"10.1080\/00029890.1989.11972155"},{"key":"2026033010152199300_j_forma-2025-0017_ref_003","doi-asserted-by":"crossref","unstructured":"John Horton Conway and R.K. Guy. The Book of Numbers. Springer-Verlag, 1996.","DOI":"10.1007\/978-1-4612-4072-3"},{"key":"2026033010152199300_j_forma-2025-0017_ref_004","unstructured":"Leonard Eugene Dickson. History of Theory of Numbers. New York, 1952."},{"key":"2026033010152199300_j_forma-2025-0017_ref_005","doi-asserted-by":"crossref","unstructured":"Harvey Dubner and Wilfrid Keller. Factors of generalized Fermat numbers. Mathematics of Computation, 64(209):397\u2013405, 1995. doi:10.2307\/2153343.","DOI":"10.1090\/S0025-5718-1995-1270618-1"},{"key":"2026033010152199300_j_forma-2025-0017_ref_006","doi-asserted-by":"crossref","unstructured":"Adam Grabowski. Elementary number theory problems. Part VI. Formalized Mathematics, 30(3):235\u2013244, 2022. doi:10.2478\/forma-2022-0019.","DOI":"10.2478\/forma-2022-0019"},{"key":"2026033010152199300_j_forma-2025-0017_ref_007","doi-asserted-by":"crossref","unstructured":"Adam Grabowski. Elementary number theory problems. Part XII \u2013 primes in arithmetic progression. Formalized Mathematics, 31(1):277\u2013286, 2023. doi:10.2478\/forma-2023-0022.","DOI":"10.2478\/forma-2023-0022"},{"key":"2026033010152199300_j_forma-2025-0017_ref_008","doi-asserted-by":"crossref","unstructured":"Adam Grabowski, Artur Korni\u0142owicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191\u2013198, 2015. doi:10.1007\/s10817-015-9345-1.","DOI":"10.1007\/s10817-015-9345-1"},{"key":"2026033010152199300_j_forma-2025-0017_ref_009","doi-asserted-by":"crossref","unstructured":"Richard K. Guy. Unsolved Problems in Number Theory. Problem Books in Mathematics. Springer, third edition, 2004. doi:10.1007\/978-0-387-26677-0.","DOI":"10.1007\/978-0-387-26677-0"},{"key":"2026033010152199300_j_forma-2025-0017_ref_010","doi-asserted-by":"crossref","unstructured":"Michal K\u0159\u00ed\u017eek, Florian Luca, and Lawrence Somer. Factors of Fermat numbers. In 17 Lectures on Fermat Numbers: From Number Theory to Geometry, pages 70\u201379. Springer New York, 2001. doi:10.1007\/978-0-387-21850-27.","DOI":"10.1007\/978-0-387-21850-2_7"},{"key":"2026033010152199300_j_forma-2025-0017_ref_011","unstructured":"Louis J. Mordell. Diophantine Equations. Academic Press, 1969."},{"key":"2026033010152199300_j_forma-2025-0017_ref_012","doi-asserted-by":"crossref","unstructured":"Adam Naumowicz. Dataset description: Formalization of elementary number theory in Mizar. In Christoph Benzm\u00fcller and Bruce R. Miller, editors, Intelligent Computer Mathematics \u2013 13th International Conference, CICM 2020, Bertinoro, Italy, July 26\u201331, 2020, Proceedings, volume 12236 of Lecture Notes in Computer Science, pages 303\u2013308. Springer, 2020. doi:10.1007\/978-3-030-53518-622.","DOI":"10.1007\/978-3-030-53518-6_22"},{"key":"2026033010152199300_j_forma-2025-0017_ref_013","doi-asserted-by":"crossref","unstructured":"Marco Riccardi. The perfect number theorem and Wilson\u2019s theorem. Formalized Mathematics, 17(2):123\u2013128, 2009. doi:10.2478\/v10037-009-0013-y.","DOI":"10.2478\/v10037-009-0013-y"},{"key":"2026033010152199300_j_forma-2025-0017_ref_014","doi-asserted-by":"crossref","unstructured":"Colin Rothgang, Artur Korni\u0142owicz, and Florian Rabe. A new export of the Mizar Mathematical Library. In Fairouz Kamareddine and Claudio Sacerdoti Coen, editors, Intelligent Computer Mathematics, pages 205\u2013210, Cham, 2021. Springer International Publishing. doi:10.1007\/978-3-030-81097-917.","DOI":"10.1007\/978-3-030-81097-9_17"},{"key":"2026033010152199300_j_forma-2025-0017_ref_015","doi-asserted-by":"crossref","unstructured":"Andrzej Schinzel and Wac\u0142aw Sierpi\u0144ski. Sur certaines hypoth\u00e8ses concernant les nombres premiers. Acta Arithmetica, 4(3):185\u2013208, 1958.","DOI":"10.4064\/aa-4-3-185-208"},{"key":"2026033010152199300_j_forma-2025-0017_ref_016","unstructured":"Wac\u0142aw Sierpi\u0144ski. Elementary Theory of Numbers. PWN, Warsaw, 1964."},{"key":"2026033010152199300_j_forma-2025-0017_ref_017","unstructured":"Wac\u0142aw Sierpi\u0144ski. Teoria liczb. Instytut Matematyczny Polskiej Akademii Nauk, 1950. In Polish."},{"key":"2026033010152199300_j_forma-2025-0017_ref_018","unstructured":"Wac\u0142aw Sierpi\u0144ski. 250 Problems in Elementary Number Theory. Elsevier, 1970."},{"key":"2026033010152199300_j_forma-2025-0017_ref_019","doi-asserted-by":"crossref","unstructured":"Rafa\u0142 Ziobro. On subnomials. Formalized Mathematics, 24(4):261\u2013273, 2016. doi:10.1515\/forma-2016-0022.","DOI":"10.1515\/forma-2016-0022"},{"key":"2026033010152199300_j_forma-2025-0017_ref_020","doi-asserted-by":"crossref","unstructured":"Rafa\u0142 Ziobro. Application of complex classes to number theory. Formalized Mathematics, 33(1):207\u2013216, 2025. doi:10.2478\/forma-2025-0016.","DOI":"10.2478\/forma-2025-0016"}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.sciendo.com\/pdf\/10.2478\/forma-2025-0017","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T10:16:06Z","timestamp":1774865766000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.2478\/forma-2025-0017"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,1]]},"references-count":20,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12,31]]},"published-print":{"date-parts":[[2025,9,1]]}},"alternative-id":["10.2478\/forma-2025-0017"],"URL":"https:\/\/doi.org\/10.2478\/forma-2025-0017","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,1]]}}}