If $n$ be a non-negative integer then solve for $n$:$$\left\lfloor \frac{n}{27} \right\rfloor=\left\lfloor \frac{n}{28} \right\rfloor$$

My Attempt: $$\left\lfloor \frac{n}{27} \right\rfloor=\left\lfloor \frac{n}{28} \right\rfloor=k$$

I am able to get $k<28$ but can't proceed from here


marked as duplicate by Aqua algebra-precalculus Apr 21 at 15:28

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  • $\begingroup$ Plugin many different numbers for $n$, can you observe a pattern? $\endgroup$ – Imago Apr 21 at 15:23

Hint: $${n\over 28}\geq [{n\over 28}] = [{n\over 27}] > {n\over 27}-1$$

so $n< 27\cdot 28$...

Another hint: Draw a graph of $[{n\over 28}]$ and $[{n\over 27}]$.


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