x\times b\le a
\implies
x\le\dfrac{a}{b}
\iff
x \le\lfloor\dfrac{a}{b}\rfloor
x\times b < a
\implies
x\le\dfrac{a+1}{b}
\iff
x \le\lfloor\dfrac{a+1}{b}\rfloor
x\times b\ge a
\implies
x>\dfrac{a-1}{b}
\iff
x >\lfloor\dfrac{a-1}{b}\rfloor
x\times b> a
\implies
x>\dfrac{a}{b}
\iff
x >\lfloor\dfrac{a}{b}\rfloor
$\lceil\dfrac{n+1}{d}\rceil=x$ ：最小的 $x$ 使 $\lfloor\dfrac{n}{x}\rfloor< d$ 。