# Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ*

Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2008)

- Volume: 16, Issue: 2, page 103-107
- ISSN: 1426-2630

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topHiroyuki Okazaki, and Yasunari Shidama. " Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ* ." Formalized Mathematics 16.2 (2008): 103-107. <http://eudml.org/doc/266839>.

@article{HiroyukiOkazaki2008,

abstract = {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\{0is 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
},

author = {Hiroyuki Okazaki, Yasunari Shidama},

journal = {Formalized Mathematics},

language = {eng},

number = {2},

pages = {103-107},

title = { Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ* },

url = {http://eudml.org/doc/266839},

volume = {16},

year = {2008},

}

TY - JOUR

AU - Hiroyuki Okazaki

AU - Yasunari Shidama

TI - Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ*

JO - Formalized Mathematics

PY - 2008

VL - 16

IS - 2

SP - 103

EP - 107

AB - 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{0is 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

LA - eng

UR - http://eudml.org/doc/266839

ER -

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