Notation for "is divisible by"

Is there a standard way of writing $a$ is divisible by $b$ in mathematical notation?

From what I've search it seems that writing $a \equiv 0 \pmod b$ is one way? But also you can write $b \mid a$ as well (the middle character is a pipe)? And sometimes that pipe is replaced by $3$ vertical dots?

Or is there a way of writing $a$ is a multiple of $b$ which I think means the same thing?

EDIT: thanks for the answers, is there a way to extend this and write something like: $b \mid a$ when $a = k$

Solution 1:

I have seen the following:

• $b \mid a$ that is with $\LaTeX$ \mid
• $a = 0 \mod b$ that is with $\LaTeX$ \mod
• $a = 0 \pmod b$ that is with $\LaTeX$ \pmod
• $a \bmod b = 0$ that is with $\LaTeX$ \bmod
• $a \equiv 0\ (b)$
• $a \equiv_{b} 0$

and of course there is

• $a = bk$ for some $k \in \mathbb{Z}$

Choose whatever suits you (and your friends or readers) best!

Solution 2:

Alexander Merkurjev taught me a long time ago the ingenious Russian notation $6 \vdots 2$, which I immediately adopted .
It pleasantly "rhymes" with the equivalent $(6)\subset (2)$