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Lemma: Coprimality and Congruence Classes

Let $m > 0$ be a positive integer. Among the infinitely many representatives $a\in\mathbb Z$ of a given congruence class $a(m)\in\mathbb Z_m$, either all or none are co-prime to $m.$

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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