New posts in Ceiling And Floor Functions

Prove that $\forall a\in \mathbb{R\smallsetminus Q}$, there exist infinitely many $n\in \mathbb N$ such that $\lfloor{an^2}\rfloor$ is even.

Prove that $\lim\limits_{k\to\infty}\left(\frac1k\sum\limits_{n=1}^k\left\lfloor\frac kn\right\rfloor-\ln k\right)=2\gamma-1$

Analyzing $\biggl\lfloor{\frac{x}{5}}\bigg\rfloor=\bigg\lfloor{\frac{x}{7}}\bigg\rfloor$

Limit $\lim\limits_{a \to 0}( a\lfloor\frac{x}{a}\rfloor)$

A combinatorial identity with binomial coefficients and floor function.

How to find $\sum_{i=1}^n\left\lfloor i\sqrt{2}\right\rfloor$ A001951 A Beatty sequence: a(n) = floor(n*sqrt(2)).

$\lfloor a n\rfloor \lfloor b n\rfloor \lfloor c n\rfloor = \lfloor d n\rfloor \lfloor e n\rfloor \lfloor f n\rfloor$ for all $n$

Hints to find solution of : $\left\lfloor \frac{x}{100} \left\lfloor \frac{x}{100}\right\rfloor \right\rfloor=5$

When $\lfloor{ab}\rfloor = \lfloor{a}\rfloor\lfloor{b}\rfloor$

Simplifying $\sum_{i=1}^n{\lfloor \frac{n}{i} \rfloor}$?