Is there a word for $\left\lfloor\frac{x-1}{n}\right\rfloor + 1$?

Question

I'm wondering if there is a name for this quantity

$$k=\left\lfloor\frac{x-1}n\right\rfloor+1=\left\lceil\frac xn\right\rceil$$

It represents the number of boxes needed to contain $x$ objects if each box can hold up to $n$ objects. Equivalently, $kn$ is the smallest multiple of $n$ which is greater than or equal to $x$. I'm sure there are many other uses for this quantity, and I seem to run into it a lot. I've tried searching for it but haven't had any luck.

Answer 1

With your equivalent definition, you can write it more succinctly as $$k = \left\lceil\frac{x}{n}\right\rceil.$$ (Since $kn$ is the smallest multiple of $n$ which is at least $x$ $\iff$ $k$ is the smallest integer $\geqslant x/n$.)

So, "ceil of $x/n$" can work, if you count that as valid.