Simplifying floor > $ \left \lfloor{\frac{\left \lfloor{\frac{n}{2}}\right \rfloor}{2}}\right \rfloor= \left \lfloor{\frac{n}{2^2}}\right \rfloor$

Question

Is the following true

$ \left \lfloor{\frac{\left \lfloor{\frac{n}{2}}\right \rfloor}{2}}\right \rfloor= \left \lfloor{\frac{n}{2^2}}\right \rfloor$

for all $n \in \mathbb{I}$

Answer 1

Hint:

Test with $n=4a,4a+1,4a+2,4a+3$ where $a$ is an integer

For all the case

$$\left\lfloor\dfrac n4\right\rfloor=a$$

$$\left \lfloor{\frac{\left \lfloor{\frac{n}{2}}\right \rfloor}{2}}\right \rfloor=?$$