###### tags: `fiche` `S1` `maths`
<div style="display: flex; justify-content: space-between;">
<span>Version 1.0.0</span>
<span>2020/12/03</span>
</div>
<div style="height:25em"></div>
<div style="text-align:center">
<h1 style="font-size:3.5em;line-height: 2.5;">S1 Maths - Gauss Lemma : Cours</h1>
<div>
Adam Alani <a href="mailto:[e-mail]">&lt;[e-mail]&gt;</a> <br>
</div>
</div>
<div style="height:25em"></div>

----

[TOC]

----
# 1. Property

Let $(a, b, c) \in \mathbb Z^3$

$$
a | bc, gcd(a , b) = 1 \implies a | c
$$w

## 1.1. Demo
$\exists (u , v) \in \mathbb Z^2 , au + bv = 1,$

$$
\begin{align}
a | bc &\implies \exists k \in \mathbb Z | bc = ka \\
acu + bcv = c &\implies acu + kav = c \\
&\implies a( cu + kv) = c ⇒ a | c
\end{align}
$$