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→Integers modulo m: Ce to put first things first. "Group" is a digression since "cyclic group" is the important part. |
→Integers modulo m: Add explanation to make it more accessible. |
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as in the arithmetic for the 24-hour clock.
The notation <math>\mathbb{Z}/m\mathbb{Z}</math> is used because this ring is the [[quotient ring]] of <math>\mathbb{Z}</math> by the [[ideal (ring theory)|ideal]] <math>m\mathbb{Z}</math>, the set formed by all multiples of {{math|''m''}}, i.e., all numbers {{math|''k m''}} with <math>k\in\mathbb{Z}.</math>
Under addition, <math>\mathbb Z/m\Z</math> is a [[cyclic group]], and all cyclic groups are isomorphic with <math>\mathbb Z/m\mathbb Z</math> for some {{mvar|m}}.<ref>Sengadir T., {{Google books|id=nglisrt9IewC|page=293|text=Zn is generated by 1|title=Discrete Mathematics and Combinatorics}}</ref>
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