# Is there some nomenclature to get the remainder of a value?

I want to write a formula where I can say that I have to get the remainder of a division by 4.

$y = \mathbf{remainder}(x\div4)$

Is there any math nomenclature I can use?

For integer $x$, put $\,y\,$ equal to $\;\bf x \;\text{mod}\; 4\;$. The "mod" operator will return the remainder when $x$ is divided by $4$.

See, for example: remainders: Modular Arithmetic

Note: In computer programming, this is often denoted $\;x\, \%\, 4$, where $x$ is an integer.

• Nice when you add links +1 Commented Jun 10, 2013 at 0:07

You can say $y=x\pmod 4$

• That would be less ambiguously written as $\ y = (x\ {\rm mod}\ 4),\$ which avoids it being misinterpreted as $\ y\equiv x\pmod 4.$ Commented Jun 9, 2013 at 15:37
• @KeyIdeas Is that notation even used? I've never seen it. Commented Jun 9, 2013 at 15:40
• $x\ {\rm mod}\ m\$ is very widely used for the remainder function. But $\ x\ ({\rm mod}\ m)\$ often denotes the equivalence class $\ x + m\,\Bbb Z,\,$ not the remainder (though, in some contexts, they may denote the same object). Commented Jun 9, 2013 at 15:43
• @KeyIdeas I understand all those subtleties, I just never saw that notation before. Feel free to post your own answer and I'll delete mine. However I get the feeling that is sufficient for the OP. Commented Jun 9, 2013 at 15:45
• @KeyIdeas Oops, can't delete it now. The OP accepted this answer. Commented Jun 9, 2013 at 15:49