OI-Wiki：
艾佛森括号
设 \(P\) 是一个 命题，那么：
\[[P] = \begin{cases}1, P\text{ is true}\\ 0, P\text{ is false}\end{cases}
\]
数论分块
Theorem. 若 \(a, b, c\) 均为整数，那么有 \(\displaystyle \left\lfloor\dfrac{a}{bc}\right\rfloor = \left\lfloor\dfrac{\left\lfloor\dfrac{a}{b}\right\rfloor}{c}\right\rfloor\)。
令 \(r = \dfrac{a}{b} - \left\lfloor\dfrac{a}{b}\right\rfloor\)，显然 \(0 \leq r < 1\)。
\[\left\lfloor\dfrac{a}{bc}\right\rfloor = \left\lfloor\frac{a}{b} \times \frac{1}{c}\right\rfloor = \left\lfloor\frac{1}{c} \times \left(\left\lfloor\frac{a}{b}\right\rfloor + r\right)\right\rfloor = \left\lfloor\dfrac{\left\lfloor\dfrac{a}{b}\right\rfloor}{c} + \frac{r}{c}\right\rfloor = \left\lfloor\dfrac{\left\lfloor\dfrac{a}{b}\right\rfloor}{c}\right\rfloor
\]