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http://hdl.handle.net/11320/11413
Tytuł: | Elementary Number Theory Problems. Part II |
Autorzy: | Korniłowicz, Artur Surowik, Dariusz |
Słowa kluczowe: | number theory divisibility primes |
Data wydania: | 2021 |
Data dodania: | 30-sie-2021 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 29, Issue 1, Pages 63-68 |
Abstrakt: | In this paper problems 14, 15, 29, 30, 34, 78, 83, 97, and 116 from [6] are formalized, using the Mizar formalism [1], [2], [3]. Some properties related to the divisibility of prime numbers were proved. It has been shown that the equation of the form p2 + 1 = q2 + r2, where p, q, r are prime numbers, has at least four solutions and it has been proved that at least five primes can be represented as the sum of two fourth powers of integers. We also proved that for at least one positive integer, the sum of the fourth powers of this number and its successor is a composite number. And finally, it has been shown that there are infinitely many odd numbers k greater than zero such that all numbers of the form 22n + k (n = 1, 2, . . . ) are composite. |
Afiliacja: | Artur Korniłowicz - Institute of Informatics, University of Białystok, Poland Dariusz Surowik - University of Białystok, Poland |
URI: | http://hdl.handle.net/11320/11413 |
DOI: | 10.2478/forma-2021-0006 |
ISSN: | 1426-2630 |
e-ISSN: | 1898-9934 |
metadata.dc.identifier.orcid: | 0000-0002-4565-9082 0000-0003-2288-8138 |
Typ Dokumentu: | Article |
metadata.dc.rights.uri: | https://creativecommons.org/licenses/by-sa/3.0/ |
Właściciel praw: | © 2021 University of Białymstoku CC-BY-SA License ver. 3.0 or later |
Występuje w kolekcji(ach): | Artykuły naukowe (WFiloz) Artykuły naukowe (WInf) Formalized Mathematics, 2021, Volume 29, Issue 1 |
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