I'm looking for the meaning of this line: $q_i | 1$.
It should be related to dividers of a number or prime numbers.
If this is not enough information then please leave a comment because the proof it's from is written in dutch so I'll need to translate it first before I can show it.
I tried looking for this on the web and on stackexchange but the search functions don't search for | so I'm not able to find my probably simple answer.
$a|b$ means $a$ divides $b$, or rather $b$ is divisible by $a$. This means that $b=aq$ for some $a, q \in \mathbb{Z}$. The restriction that $a,q$ should be integers depends on the fields of mathematics you are in, and some times is not present.
For example, $5|15$, i.e. $5$ divides $15$, or $15$ is divisible by $5$. In deed, $15=5*3$. In this case, $a=5$, $b=15$, $q=3$.
In the universe of integer numbers, $q_1|1$ implies that $q_1=\pm1$. It is in deed the case that $1$ is only divisible by itself and $-1$. If you are studying discrete mathematics, for example, which only deals with integers, this is the meaning of it.