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Proposition: Creation of Reduced Residue Systems From Others

Let $m > 0$ be a positive integer and let $n\perp m$ be co-prime. If $R=\{a_1,\ldots,a_{\phi(m)}\}$ is a reduced residue system modulo $m$, then $nR:=\{na_1,\ldots,na_{\phi(m)}\}$ is also a reduced residue system modulo $m.$

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3
Propositions: 4

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References

Bibliography

  1. Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927
  2. Jones G., Jones M.: "Elementary Number Theory (Undergraduate Series)", Springer, 1998