Going through a proof of a theorem, I encountered the following statement:
$e\mid a/d$, $e\mid b/d$
Then, $a/d = ex$, $b/d = ey$ where $x,y$ belongs to $\mathbb{Z}$.
However, my question not about the proof of the theorem.
My question is, what does the sign ' $\mid$ ' mean?
The symbol $\mid$ means "divides" (in this context, at least). That is, if $a$ and $b$ are integers then $a\mid b$ (read "$a$ divides $b$") means that there exists an integer $c$ such that $b=ac$. Except in the case $a=b=0$, this just means that $b/a$ is an integer. (More generally, you can make the same definition for elements of any ring.)