# LaTeX symbol for “divides precisely”

I sometimes need to write that a certain prime p^k precisely divides a number n, meaning that p^k | m but it is not the case that p^{k+1} | m. It is often written as: p^k || m, where the symbol in the middle is supposed to look like a pair of vertical lines close to one another.

Is there a good way to write this in LaTeX? I am aware of the following possibilities, none of which is fully satisfactory:

1. p^k \Vert n gives a nice pair of vertical lines, but the spacing looks wrong.
2. p^k \mid\mid n gives the right spacing between numbers and the symbol, but the lines are very far apart.
3. p^k \mid \!\!\: \mid n and p^k \ \Vert \ n look about right, but I hear that manually adding spacing is sometimes risky.

Are there any better possibilities?

You might use \parallel, which produces the same symbol as \Vert, but correctly spaced for a relation symbol.

Another possibility is

\newcommand{\pdiv}{\mid\!\mid}


and $a\pdiv b$ would produce

If you choose \parallel, use a new command anyway, so you can easily change your mind later:

%\newcommand{\pdiv}{\parallel} % I'll use the next
\newcommand{\pdiv}{\mid\!\mid}


There's nothing wrong in using explicit spaces, so long as you know what you're doing. Surely \: is not the right spacing command to use, because it introduces a flexible space. If you feel that \mid\!\mid is too tight, try

\mid\mspace{-2mu}\mid


(requires amsmath); the command \! backs up by 3mu, while the natural space component of \: is 4mu, so \!\!\: has a natural width of –2mu. But \mspace{-2mu} has no flexibility.

Here is a comparison: first row \mid\!\mid; second row \mid\mspace{-2mu}\mid, third row \parallel

If I had to choose, I'd select the first one. But with a new command you're not bound to a decision until the last time.

Although it looks strange, you need \parallel:

\documentclass{article}

\begin{document}

$p^k\parallel n$

$p^k \mid \!\!\: \mid n$ and $p^k \ \Vert \ n$

\end{document}