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http://hdl.handle.net/11320/21008| Tytuł: | Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ |
| Autorzy: | Okazaki, Hiroyuki Shidama, Yasunari |
| Data wydania: | 2008 |
| Data dodania: | 14-wrz-2026 |
| Wydawca: | University of Białystok |
| Źródło: | Formalized Mathematics, Volume 16, Issue 2, 2008, Pages 103-107 |
| Abstrakt: | In the [20], it had been proven that the Integers modulo p, in this article we shall refer as Z/pZ, constitutes a field if and only if p is a prime. Then the prime modulo Z/pZ is an additive cyclic group and Z/pZ∗ = Z/pZ\{0} is a multiplicative cyclic group, too. The former has been proven in the [23]. However, the latter had not been proven yet. In this article, first, we prove a theorem concerning the LCM to prove the existence of primitive elements of Z/p∗. Moreover we prove the uniqueness of factoring an integer. Next we define the multiplicative group Z/pZ∗ and prove it is cyclic. |
| Afiliacja: | Hiroyuki Okazaki - Shinshu University Nagano, Japan Yasunari Shidama - Shinshu University Nagano, Japan |
| URI: | http://hdl.handle.net/11320/21008 |
| DOI: | 10.2478/v10037-008-0015-1 |
| ISSN: | 1426-2630 |
| e-ISSN: | 1898-9934 |
| Typ Dokumentu: | Article |
| metadata.dc.rights.uri: | https://creativecommons.org/licenses/by-sa/4.0/ |
| Właściciel praw: | © 2009 Hiroyuki Okazaki, Yasunari Shidama, published by University of Białystok This work is licensed under the Creative Commons License |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2008, Volume 16, Issue 2 |
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| Uniqueness_of_Factoring_an_Integer_and_Multiplicative_Group_ZpZ.pdf | 262,05 kB | Adobe PDF | Otwórz |
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