How to prove this floor function equation?
1449
Floor function properties: $[2x] = [x] + [ x + \frac12 ]$ and $[nx] = \sum_{k = 0}^{n - 1} [ x + \frac{k}{n} ] $
158395
Find $\lfloor {\alpha}^6 \rfloor$
59462
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
143819
Supremum of $\sqrt{n} -\left\lfloor\sqrt{n}\right\rfloor $
143540
How to prove this decomposition of sum of squares?
13098
Find a formula for $\sum\limits_{k=1}^n \lfloor \sqrt{k} \rfloor$
114889
Solve summation $\sum_{i=1}^n \lfloor e\cdot i \rfloor $
158463
Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$
82001
How to prove the function is a constant
40779
What is the smallest possible value of $\lfloor (a+b+c)/d\rfloor+\lfloor (a+b+d)/c\rfloor+\lfloor (a+d+c)/b\rfloor+\lfloor (d+b+c)/a\rfloor$?
40973
How to find $\lfloor 1/\sqrt{1}+1/\sqrt{2}+\dots+1/\sqrt{100}\rfloor $ without a calculator?
101641
Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$
106191
Integrating Floor Functions
142338
Prove that $\lfloor\frac{n+1}{2}\rfloor+\lfloor\frac{n+2}{4}\rfloor+\lfloor\frac{n+4}{8}\rfloor+\lfloor\frac{n+8}{16}\rfloor+ \dots=n$
78356
How to prove ${n \choose p} \equiv\left\lfloor \frac{n}{p} \right\rfloor\pmod p$
30639
Efficient computation of $\sum_{k=1}^n \left\lfloor \frac{n}{k}\right\rfloor$
91684
Prove the following equation(much needed help):