Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $a = k$

share|improve this question
    
I usually use $|$ –  Belgi Apr 22 '12 at 12:48
    
The standard is $b\mid a$ whic is typeset "b \mid a" in TeX –  Andrea Mori Apr 22 '12 at 12:54
    
    
@pedja, thanks but that article lists both options –  Jonathan. Apr 22 '12 at 13:03
1  
@PeterPhipps The spacing is different, compare $A|B$, $A\mid B$, $A\vert B$, $A\lvert B$ and $A\rvert B$ (edit: there actually are differences there in some fonts, even if those are not visible here). –  dtldarek Apr 22 '12 at 13:17

5 Answers 5

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!

share|improve this answer
    
Thanks for the list, a mod b = 0 makes the most sense to me. But b|a seems more for use in commentary? –  Jonathan. Apr 22 '12 at 13:19
1  
It depends on so many things that I can't tell you this or that way. For me there are three important factors: how often will I use it (more often means less symbols), do I need to use it "in chains" like $a = b = c = d \pmod n$ and do I need to use different $n$-s, e.g. $a \equiv_3 b \equiv_5 c \equiv_7 d$ (which may be confusing but sometimes is helpful). Still, the most important criterion of all is readability. –  dtldarek Apr 22 '12 at 13:26

There is also " $a \in b\mathbb Z$ ".

share|improve this answer

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 $(6)\subset (2)$

share|improve this answer
1  
I wonder if you are the unique non-Russian who uses that notation. I didn't think it is used in public outside of Russia (or at least Eastern Europe). –  KCd Jan 22 '13 at 13:48

I often write that as b divides a

Notation:

$$b \mid a$$

share|improve this answer
1  
This is the standard way, in the specific meaning of compliance to international standards: ISO 80000-2, clause 2.7-17. Note that the vertical bar character used there is normatively identified as U+2223 DIVIDES (∣), note the common U+007C VERTICAL LINE (|) that we enter directly on a keyboard. It is of course possible to express the same thing using a congruence notation, but only for integers (not e.g. for polynomials). –  Jukka K. Korpela Jun 22 '12 at 5:09

$a \equiv 0 \mod b$ and $b \mid a$ are both common, and their use depends on the context. Given a choice, I use the latter more than the former.

There are others such as $\text{lcm}(a,b)=a$ or $\text{hcf}(a,b)=b$ [or perhaps $\text{gcd}(a,b)=b$ if you prefer] which might also be used when more suitable for the context.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.