Product on Greatest integer

Question

I want to prove the following equality: $\left[\frac{[x]}{n}\right] = \left[\frac{x}{n} \right]$, if $n \in \mathbb{N}$. I did it: $$h = \left[\frac{[x]}{n}\right] \rightarrow h\leq \frac{x}{n}< h + 1$$ For definition of greatest integer: $$h \leq \left[\frac{x}{n} \right] $$ How to prove: $h \geq \left[\frac{x}{n} \right] $

Answer 1

Hint: ${x-[x] \over n}<{1 \over n}$ and ${[x] \over n} \in \mathbb Q$.