The Structure of U(ℤ/nℤ)

Having introduced the notion of congruence and discussed some of its properties and applications we shall now go more deeply into the subject. The key result is the existence of primitive roots modulo a prime. This theorem was used by mathematicians before Gauss but he was the first to give a proof....

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Bibliographic Details
Published inA Classical Introduction to Modern Number Theory pp. 39 - 49
Main Authors Ireland, Kenneth, Rosen, Michael
Format Book Chapter
LanguageEnglish
Published New York, NY Springer New York 19.10.2012
SeriesGraduate Texts in Mathematics
Subjects
Cyclic Group
Distinct Root
Finite Subgroup
Primitive Root
Riemann Hypothesis
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ISBN9781441930941
1441930949
ISSN0072-5285
2197-5612
DOI10.1007/978-1-4757-2103-4_4

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Summary:Having introduced the notion of congruence and discussed some of its properties and applications we shall now go more deeply into the subject. The key result is the existence of primitive roots modulo a prime. This theorem was used by mathematicians before Gauss but he was the first to give a proof. In the terminology introduced in Chapter 3 the existence of primitive roots is equivalent to the fact that U(ℤ/pℤ) is a cyclic group when p is a prime. Using this fact we shall find an explicit description of the group U(ℤ/nℤ) for arbitrary n.
ISBN:9781441930941
1441930949
ISSN:0072-5285
2197-5612
DOI:10.1007/978-1-4757-2103-4_4