# $\lfloor \frac{n}{27} \rfloor=\lfloor \frac{n}{28} \rfloor$ [duplicate]

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

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

## 1 Answer

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 $$[{n\over 27}]$$.