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Formalized Mathematics

(a computer assisted approach)

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Volume 16, Issue 2

Issues

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

Hiroyuki Okazaki / Yasunari Shidama
Published Online: 2009-03-20 | DOI: https://doi.org/10.2478/v10037-008-0015-1

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

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

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About the article


Published Online: 2009-03-20

Published in Print: 2008-01-01


Citation Information: Formalized Mathematics, Volume 16, Issue 2, Pages 103–107, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-008-0015-1.

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[1]
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