Ceiling / floor conversion formula

Question

Here one can see the following formula:

for $m\ne 0$. However, if $m=1$ then we have $\lceil n\rceil = \lfloor n\rfloor$. So does this mean that Wikipedia is missing this condition that $m$ must be $\ge 2$?

Answer 1

From the start of the section:

In the following formulas [...] $k$, $m$, and $n$ are integers

The formulas you derived for $m=1$ clearly hold for $n \in \Bbb Z$, so no problem arises.