Uniqueness of Factoring an Integer and Multiplicative GroupZ/pZ*

• Autorzy: Hiroyuki Okazaki , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

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 Z/pZ 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/pZ*. Moreover we prove the uniqueness of factoring an integer. Next we define the multiplicative group Z/pZ* and prove it is cyclic.MML identifier: INT 7, version: 7.8.10 4.99.1005

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2008
• Tom: 16
• Numer: 2
• Strony: 103-107

Daty

wydano

2008-01-01

online

2009-03-20

Twórcy

autor

Hiroyuki Okazaki

• Shinshu University, Nagano, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

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Identyfikatory

DOI

10.2478/v10037-008-0015-1