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The selected problems are: 108, 112\u2013114, 118\u2013119, 127, 129, 130, and 132\u2013134 formalized in the Mizar system.\n                  <\/jats:p>","DOI":"10.2478\/forma-2025-0020","type":"journal-article","created":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T16:26:28Z","timestamp":1767975988000},"page":"245-265","source":"Crossref","is-referenced-by-count":0,"title":["Elementary Number Theory Problems. Part XIX"],"prefix":"10.2478","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7099-1669","authenticated-orcid":false,"given":"Karol","family":"P\u0105k","sequence":"first","affiliation":[{"name":"Faculty of Computer Science , University of Bia\u0142ystok , Poland"}]}],"member":"374","published-online":{"date-parts":[[2025,12,31]]},"reference":[{"key":"2026033010152245923_j_forma-2025-0020_ref_001","doi-asserted-by":"crossref","unstructured":"P.T. Bateman, J.L. Selfridge, and S.S. Wagsta Jr. The editor\u2019s corner: The new Mersenne conjecture. 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Springer, 2020. doi:10.1007\/978-3-030-53518-622.","DOI":"10.1007\/978-3-030-53518-6_22"},{"key":"2026033010152245923_j_forma-2025-0020_ref_014","doi-asserted-by":"crossref","unstructured":"Karol P\u0105k. Elementary number theory problems. Part XVI. Formalized Mathematics, 32 (1):203\u2013212, 2024. doi:10.2478\/forma-2024-0017.","DOI":"10.2478\/forma-2024-0017"},{"key":"2026033010152245923_j_forma-2025-0020_ref_015","unstructured":"Wac\u0142aw Sierpi\u0144ski. Elementary Theory of Numbers. PWN, Warsaw, 1964."},{"key":"2026033010152245923_j_forma-2025-0020_ref_016","unstructured":"Wac\u0142aw Sierpi\u0144ski. Teoria liczb. Instytut Matematyczny Polskiej Akademii Nauk, 1950. In Polish."},{"key":"2026033010152245923_j_forma-2025-0020_ref_017","unstructured":"Wac\u0142aw Sierpi\u0144ski. 250 Problems in Elementary Number Theory. Elsevier, 1970."}],"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.sciendo.com\/pdf\/10.2478\/forma-2025-0020","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T10:15:45Z","timestamp":1774865745000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.2478\/forma-2025-0020"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,1]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12,31]]},"published-print":{"date-parts":[[2025,9,1]]}},"alternative-id":["10.2478\/forma-2025-0020"],"URL":"https:\/\/doi.org\/10.2478\/forma-2025-0020","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,1]]}}}