$x\le\lceil\sqrt{x}\rceil\left\lceil\frac{x}{\lceil\sqrt{x}\rceil}\right\rceil$
How do I show this?
I made a plot, and it looks true:
$x\le\lceil\sqrt{x}\rceil\left\lceil\frac{x}{\lceil\sqrt{x}\rceil}\right\rceil$
How do I show this?
I made a plot, and it looks true:
Hint: $\frac{x}{\lceil\sqrt{x}\rceil} \leq \lceil\frac{x}{\lceil\sqrt{x}\rceil}\rceil$.
Divide both sides by $\lceil \sqrt x\rceil$.