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title: 1. Property
tags: [maths, S1, fiche]

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###### tags: `fiche` `S1` `maths`
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  <span>Version 1.0.0</span>
  <span>2020/12/03</span>
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	<h1 style="font-size:3.5em;line-height: 2.5;">S1 Maths - Gauss Lemma : Cours</h1>
	<div>
          Adam Alani <a href="mailto:adam.alani@epita.fr">&lt;adam.alani@epita.fr&gt;</a> <br>
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# 1. Property
 
Let $(a, b, c) \in \mathbb Z^3$
 
$$
a | bc, gcd(a , b) = 1 \implies a | c
$$w
 
## 1.1. Demo
$\exists (u , v) \in \mathbb Z^2 , au + bv = 1,$
 
$$
\begin{align}
a | bc &\implies \exists k \in \mathbb Z | bc = ka \\
acu + bcv = c &\implies acu + kav = c \\
              &\implies a( cu + kv) = c ⇒ a | c
\end{align}
$$