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Proposition: Multiplication of Congruences with a Positive Factor

Let $a,b$ be integers and $c > 0, m > 0$ be positive integers. Then $$\begin{array}{c}a(m)\equiv b(m)\\ \Longleftrightarrow\\(ac)(mc)\equiv(bc)(mc). \end{array}$$

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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