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