TITLE: What does double vertical lines $\|$ mean in number theory?
QUESTION [6 upvotes]: I'm reading the 2002 paper P is in PRIMES and I stumbled upon this symbol $\|$ in the chapter 2:

Suppose $n$ is composite. Consider a prime $q$ that is a factor of $n$ and
  let $q^k\ ||\ n$. Then $q^k$ does not divide $n \choose q$ and is coprime to $a^{n−q}$ and hence the coefficient of $X^q$ is not zero $(\mod n\ )$. Thus $((X + a)^n − (X^n + a))$ is not identically zero over $Z^n$.

I am very new to number theory and it is not mentioned anywhere in the paper what $\|$ denotes. I tried looking it up in the Wikipedia List of mathematical symbols but I couldn't find anything.
Does anyone know what $\|$ means in this context?

REPLY [8 votes]: It means that $q^k$ fully divides $n,$ that is, $q^k$ divides $n$ but $q^{k+1}\nmid n.$